Practical  Applied    - 

ELECTRICITY 


A  BOOK  IN  PLAIN  ENGLISH 
FOR  THE  PRACTICAL  MAN. 
THEORY,  PRACTICAL  AP- 
PLICATIONS AND  EXAMPLES 


BY 
DAVID  PENN  MORETON,  B.S.,  E.E. 

ASSOCIATE     PROFESSOR     OF     ELECTRICAL     ENGINEERING     AT    ARMOUR 
INSTITUTE  OF  TECHNOLOGY,  ASSOCIATE  MEMBER  OF  THE  AMERI- 
CAN INSTITUTE  OF  ELECTRICAL   ENGINEERS,  MEMBER 
OF  THE  SOCIETY   FOR   THE   PROMOTION   OF 
ENGINEERING   EDUCATION,   ETC. 


ILLUSTRATED 


The  Reilly  &  Britton  Co. 
Chicago 


COPYRIGHT,    1911,    1913,    1916 

By   DAVID   PENN   MORETON 

CHICAGO 


PREFACE   TO   THE   THIRD    EDITION 

In  bringing  out  the  third  edition  of  Practical  Applied 
Electricity,  the  body  of  the  book,  with  the  exception  of  a 
few  minor  changes,  remains  the  same  as  in  the  second 
edition.  Several  pages  of  material,  giving  a  summary  of  the 
more  common  direct-  and  alternating-current  relations,  have 
been  added  at  the  back  of  the  book. 

This  book  is  intended  primarily  for  those  persons  who  are 
desirous  of  obtaining  a  practical  knowledge  of  the  subject  of 
Electricity,  but  are  unable  to  take  a  complete  course  in  Elec- 
trical Engineering.  It  is  the  opinion  of  the  author  that  such 
persons  should  have  a  thorough  understanding  of  the  funda- 
mental principles  of  the  subject,  in  order  that  they  may  easily 
understand  the  applications  in  practice.  Numerous  examples 
are  solved  throughout  the  book,  which  serve  to  illustrate  the 
practical  application  of  certain  laws  and  principles  and  give 
the  reader  an  opportunity  to  more  readily  grasp  their  true 
significance. 

The  text  is  based,  to  a  certain  extent,  upon  a  series  of  lec- 
.tures  given  in  the  evening  classes  in  the  Department  of  Elec- 
trical Engineering  at  Armour  Institute  of  Technology.  The 
arrangement  is  not  the  one  usually  followed,  and  to  some  it 
may  not  appear  to  be  logical;  but  it  is  one  the  author  has 
found  very  satisfactory. 

Although  the  book  was  not  originally  intended  to  be  used 
as  a  text-book,  it  is,  however,  especially  adapted  for  use  in  the 
practical  courses  given  in  the  various  High  and  Manual  Train- 
ing Schools,  and  at  the  same  time  gives  a  substantial  ground- 
work for  the  more  advanced  college  and  university  courses. 

The  author  wishes  to  express  his  thanks  to  the  various  man- 
ufacturing companies  who  have  been  very  kind  in  supplying 
material  and  cuts,  and  to  Professor  E.  H.  Freeman,  head  of 
the  Department  of  Electrical  Engineering  of  Armour  Insti- 
tute of  Technology,  for  a  number  of  valuable  suggestions. 

DAVID  PENN  MORETON 
ARMOUR  INSTITUTE  OF  TECHNOLOGY 


389482 


DEDICATED 

TO  MY 

FATHER  AND  MOTHER 
CHARLES  BROWN  MORETON 

AND 

SALLIE  PENN jMORETON 

IN 

APPRECIATION  OF  THEIR  UNTIRING 
EFFORTS  WHILE  I  WAS  RE- 
CEIVING MY  EARLY 
EDUCATION 


CONTENTS 


I      ELECTRICAL    CIRCUIT    AND    ELECTRICAL 
UNITS 

II      CALCULATION  OF  RESISTANCE 

III  SERIES  AND  DIVIDED  CIRCUITS,  MEASURE- 

MENT OF  RESISTANCE 

IV  PRIMARY  BATTERIES        .... 
V      MAGNETISM      ...... 

VI      ELECTROMAGNETISM         .... 

VII      ELECTROMAGNETIC     INDUCTION,   FUNDA- 
MENTAL  THEORY   OF   THE    DYNAMO 

VIII      ELECTRICAL  INSTRUMENTS  AND  EFFECTS 
OF  A  CURRENT  .... 

IX      DIRECT- CURRENT  GENERATOR 
X      DIRECT- CURRENT  MOTORS 

XI      ARMATURES  FOR  DIRECT-CURRENT  DYNA- 
MOS ...... 

XII      STORAGE      BATTERIES,    THEIR    APPLICA- 
TIONS AND  MANAGEMENT 

XIII  DISTRIBUTION  AND  OPERATION 

XIV  DISEASES    OF    DIRECT-CURRENT    DYNA- 

MOS   

XV  ELECTRIC  LIGHTING        .... 

XVI  ELECTRIC  WIRING            .... 

XVII  ALTERNATING-CURRENT  CIRCUIT     . 

XVIII  ALTERNATING-CURRENT  MACHINERY 

XIX  RESUSCITATION        ..... 

XX  LOGARITHMS    AND    REFERENCE    TABLES 


34 

58 
77 
86 

102 

121 
166 
193 

219 

237 
257 

280 
294 
316 
332 
358 
386 
390 


PRACTICAL  APPLIED  ELECTRICITY 


CHAPTER  I 

THE    ELECTRICAL    CIRCUIT    AND    ELECTRICAL     UNITS 

1.  Electricity. — There    are    certain    phenomena    of    nature 
that  are  taking  place  about  us  every  day  which  we  call  elec- 
trical, and  to  that  which  produces  these  phenomena  we  give 
the  name  electricity.     The  exact  nature  of  electricity  is  not 
known,  yet  the  laws  governing  its  action,  under  various  con- 
ditions, are  well  understood,  just  as  the  laws  of  gravitation 
are  known,   although   we   cannot   define   the   constitution   of 
gravity.     Electricity   is   neither   a   gas   nor   a   liquid;    its   be- 
havior sometimes  is  similar  to  that  of  a  fluid  so  that  it  is 
said  to  flow  through  a  wire.    This  expression  of  flowing  does 
not  really  mean  there  is  an  actual  movement  in  the  wire, 
similar  to  the  flow  of  water  in  a  pipe,  when  it  possesses  elec- 
trical properties,,  but  is  simply  a  convenient  expression  for 
the  phenomena  involved.     According  to  the  modern  electron 
theory  of  electricity,  there  is  a  movement  of  some  kind  tak- 
ing place  in  the  circuit,  but  the  real  nature  of  this  move- 
ment is  not  as  yet  very  well  understood.  A  great  many  electrical 
problems  can  be  easily  understood  by  comparing  them  to  a 
similar  hydraulic  problem,  where  the  relation  of  the  various 
quantities  and   the  results   are  apparent   under  given   condi- 
tions, and  on  account  of  the  similarity  of  the  two,  the  hy- 
draulic  analogy  will  often  be  used  to  illustrate  what  actu- 
ally takes  place  in  the  electrical  circuit. 

2.  Electrical  Circuit. — The  electrical  circuit  is  the  path  in 
which  the  electricity  moves.    The  properties  of  electrical  cir- 
cuits and  the  electrical  quantities  associated  with  them  make 
an   appropriate    beginning   for    the    study   of    the    subject   of 
electrical  engineering,  for  electrical  energy  is  in  almost  all 

1 


2  •:   •'    •*."    T-RACT.^CAE  APPLIED  ELECTRICITY 

practical  applications  utilized  in  circuits.  These  circuits  are 
of  various  forms  and  extent,  and  are  made  for  many  different 
purposes,  but  all  possess  to  a  greater  or  less  extent  the  same 
properties  and  involve  the  same  electrical  quantities.  Sup- 
pose, for  example,  a  door  bell  that  is  operated  from  two 


Battery 


Push  Button 


Bell 


Fig.  1 


or  three  dry  cells,  as  shown  in  Fig.  1.  This  combination 
forms  an  electrical  circuit,  typical  of  all  electrical  cir- 
cuits. It  contains  a  source  of  electrical  energy  (the  bat- 
tery), an  energy  transforming  device  (the  bell),  and  the 
necessary  connecting  materials  (wire  and  push  button).  It 
is  closed  upon  itself  and  like  the  circumference  of  a  circle 
has  neither  beginning  nor  end.  (A  table  of  symbols  com- 
monly used  in  representing  the  different  pieces  of  electrical 
apparatus  is  given  in  Chapter  20.) 

3.  Hydraulic  Analogy  of  the  Electrical  Circuit.— Before  con- 
sidering the  relation  of  the  various  electrical  quantities  asso- 
ciated with  the  electric  circuit  it  would,  no  doubt,  be  best 
to  make  a  brief  study  of  a  simple  hydraulic  problem,  simi- 
lar to  the  electrical  circuit,  and  the  relation  of  the  various 
quantities  involved.  It  must  be  clearly  understood  that  the 
similarity  between  the  water  and  the  electrical  circuits  is  in 
regard  to  action  only,  and  does  not  in  any  way  imply  an 
identity  between  electricity  and  water.  A  simple  hydraulic 
circuit  is  shown  in  Fig.  2,  where  (P)  is  a  pump  that  sup- 
plies water,  under  a  constant  pressure,  to  the  pipe  (T).  The 
water  is  conducted  through  the  pipe  (T)  to  the  tank  (K), 
the  amount  of  water  flowing  through  the  pipe  being  regu- 
lated by  the  valve  (V).  The  pipe  (T)  is  composed  of  a 
number  of  different  pieces  of  pipe,  differing  in  area  of 


THE  ELECTEICAL  CIRCUIT 


3 


cross-section,  length,  and  condition  of  their  inner  surface, 
some  being  rough  and  some  smooth.  Pressure  gauges  (Gj, 
G2,  etc.)  are  placed  along  the  pipes  at  certain  intervals,  as 
shown  in  the  figure,  to  indicate  the  pressure  in  the  pipe  at 
different  points.  Assume,  first,  that  the  valve  (V)  is  closed; 
no  water  will  then  be  flowing  through  the  pipe  and  all  of 
the  various  pressure  gauges  will  indicate  the  same  pressure 
in  the  pipe.  Assume,  as  a  second  condition,  that  the  valve  (V) 
is  partly  opened;  there  will  be  a  flow  of  water  in  the  pipe, 
and  the  pressure  gauges  will  indicate  a  different  pressure, 
their  indications  decreasing  as  you  pass  along  the  pipe, 
starting  from  the  end  attached  to  the  pump.  Opening  the 


K- 


Fig.  2 

valve  still  more  will  increase  the  flow  of  water  and  also 
the  difference  in  indications  of  the  various  gauges.  If  the 
gauge  (Ge)  at  the  end  of  the  pipe  indicates  zero  pressure, 
it  is  apparent  that  the  total  pressure  supplied  by  the  pump 
has  all  been  used  in  forcing  the  water  through  the  pipe.  If, 
on  the  other  hand,  the  last  gauge  indicates  a  certain  pres- 
sure, then  the  total  pressure  supplied  by  the  pump  has  not  all 
been  used  and  there  still  remains  a  certain  amount,  neg- 
lecting that  pressure  required  to  force  the  water  through 
the  valve  (V),  that  could  be  used  in  driving  a  water  wheel, 
placed  in  such  a  position  that  the  water  could  strike  against 
the  buckets  on  the  wheel  and  cause  it  to  rotate.  The  differ- 


4  PRACTICAL  APPLIED  ELECTRICITY 

ence  in  pressure  indicated  by  any  two  gauges  is  a  meas- 
ure of  the  pressure  required  to  cause  the  water  to  flow  be- 
tween the  two  points  where  the  gauges  are  connected  to  the 
pipe.  If  it  were  possible  to  have  a  pipe  that  would  offer  no 
opposition  to  the  passage  of  the  water  through  it,  there  would 
be  no  difference  in  the  indications  of  the  various  gauges  and 
the  water  would  flow  from  the  end  of  the  pipe  under  the 
same  pressure  as  that  produced  by  the  pump.  Anything  that 
increases  the  opposition  to  the  flow  of  the  water  will  increase 
the  value  of  the  pressure  required  to  cause  a  certain  quan- 
tity to  pass  through  the  section  of  pipe,  between  the  pres- 
sure gauges,  whose  indications  are  being  noted.  Qr,  if  the 
same  pressure  is  maintained  over  a  given  section  and  its 
opposition  to  the  passage  of  water  is  increased,  the  quantity 
passing  in  a  given  time  will  be  decreased;  similarly  the 
quantity  will  be  increased  if  the  opposition  is  decreased. 
As  an  example,  suppose  a  water  motor  is  connected  in  the 
pipe  (T)  and  it  is  perfectly  free  to  turn,  there  will  then  be  a 
very  small  pressure  required  to  cause  a  certain  quantity  to 
flow  through  the  motor  in  a  given  time.  If,  however,  the 
water  motor  is  loaded,  it  will  offer  a  much  greater  resist- 
ance to  the  passage  of  water  through  it;  and,  if  the  pres- 
sure remains  constant,  the  quantity  passing  in  a  given  time 
will  be  decreased.  The  rate  of  flow  can  be  maintained 
constant  when  the  opposition  increases  by  increasing  the 
pressure.  The  total  pressure  supplied  by  the  pump  will  be 
distributed  over  the  various  sections  of  the  pipe  in  propor- 
tion td  their  opposition.  The  opposition  offered  by  the  pipe 
can  be  called  its  resistance  and  it  will  depend  upon  the 
area,  length,  nature  of  the  inner  surface,  and  any  obstruc- 
tion that  might  be  in  the  pipe,  such  as  sand,  gravel,  or  sieves. 
The  quantity  of  water  passing  a  given  point  in  a  pipe  in  a 
unit  of  time,  usually  one  second,  is  called  the  current.  These 
three  quantities,  pressure,  current,  and  resistance,  are  related 
to  each  other  in  a  very  simple  way,  as  can  be  seen  from 
the  above  problem,  and  this  relation,  expressed  in  the  form 
of  an  equation  is: 

Pressure 

Current  =  —  (1) 

Resistance 


THE  ELECTRICAL  CIRCUIT  5 

It  must  be  remembered  that  this  equation  does  not.  hold 
in  its  strictest  sense  for  the  hydraulic  problem,  but  will 
serve  to  illustrate  the  relation  between  the  electrical  quan- 
tities that  are  to  be  discussed  in  one  of  the  following  sections. 

4.  Electrical  Circuit  Compared  with  Hydraulic  Circuit. — 
In  the  electrical  circuit,  as  indicated  in  Fig.  3,  there  is  a 
source  of  electrical  pressure,  the  battery,  that  corresponds 
to  the  pump  in  the  hydraulic  analogy.  The  wire  by  means 
of  which  the  electricity  is  conducted  corresponds  in  the 
hydraulic  analogy  to  the  pipe  through  which  the  water  flows, 


D 

1  l^J         oH   75-^ 

B 

I 

Fig.  3 

while  the  electric  motor  (M),  in  Fig.  3,  corresponds  to  the 
water  motor  referred  to  in  the  example  under  section  (3).  If 
all  the  electrical  pressure  is  consumed  in  causing  a  given 
quantity  of  electricity  to  flow  through  the  wire  in  a  given 
time,  there  will  be  no  pressure  available  to  operate  the  elec- 
trical motor  or  any  other  electrical  device,  just  as  there  would 
be  no  pressure  available  to  operate  the  water  motor  in  the 
hydraulic  problem  when  all  the  pressure  was  used  in  caus- 
ing the  water  to  flow  through  the  pipe.  The  difference  in 
electrical  pressure  between  any  two  points  on  the  wire  is  a 
measure  of  the  pressure  required  to  cause  a  given  quantity 
of  electricity  to  pass  from  one  of  the  points  to  the  other 
in  a  given  time.  This  difference  in  pressure  will  depend 
upon  the  opposition  offered  by  the  circuit  between  the  two 
points  and  the  quantity  passing  between  them  in  a  given 
time.  With  an  increase  in  the  opposition  offered  by  the  cir- 
cuit there  must  be  an  increase  in  pressure  to  maintain  a 
constant  flow.  If,  on  the  other  hand,  the  pressure  remains 
constant  and  the  opposition  to  the  flow  increases  or  decreases, 
there  will  be  a  decrease  or  increase  in  the  quantity  of 


6  PKACT1CAL  APPLIED  ELECTKICITY 

electricity  passing  a  certain  point  in  the  circuit  in  a  given 
time. 

5.  Electrical  Quantities. — There  are  three  electrical  quan- 
tities associated  with  the  electrical  circuit  that  correspond 
to  those  given  for  the  hydraulic  analogy.     These  quantities 
are  the  current  of  electricity,  the  electromotive  force  which 
causes  the  current,  and  the  resistance  which  hinders  the  free 
flow  of  the  electricity. 

6.  Current   of    Electricity. — The   rate  at  which   the   move- 
ment, or  flow,  of  electricity  takes  place  is  the  current — tor 
a  uniform  movement  it  is  the  amount  of  electricity  flowing 
per  unit  of  time — usually  the  second.     The  unit  quantity  of 
electricity  is   the   coulomb,   and   if  the  rate   of  flow  is   such 
that  one   coulomb   flows  per   second,  there   is   said   to  be   a 
current  of  one  ampere. 

At  any  instant  the  current  is  the  same  at  all  parts  of  a 
circuit  having  no  branches,  and  it  is  the  same  for  all  points 
in  each  branch,  where  there  are  branches.  A  mistake  is 
often  made  in  thinking  that  the  current  is  used  up — that 
there  is  practically  no  current  returning  to  the  source  of 
the  electrical  energy.  Such  a  condition  is  not  true.  The 
current  in  the  return  conductor  to  the  battery  or  dynamo 
is  exactly  the  same  as  the  current  in  the  conductor  carry- 
ing the  electricity  from  the  battery  or  dynamo.  The  cur- 
rent that  leaves  a  motor,  lamp,  or  bell  is  no  different  in 
value  from  that  which  enters  them.  It  is  the  energy  of  the 
electricity  that  is  used  up,  just  as  it  is  the  energy  possessed 
by  the  water  that  is  imparted  to  the  water  wheel  and  causes 
it  to  rotate  without  the  water  itself  being  consumed.  The 
symbol  used  in  representing  the  current  is  the  letter  (I). 

7.  Resistance. — Resistance   is  that  property  possessed  by 
substances  which   opposes   the   free  flow   of   electricity,   but 
does  in  no  way  tend  to  cause  a  flow  in  the  opposite  direction 
to  that  in  which  the  electricity  actually  moves. 

All  substances  resist  the  movement  of  electricity  through 
them,  but  the  resistance  offered  by  some  is  very  much  greater 
than  that  offered  by  others,  and  as  a  result  all  materials 
may  be  grouped  under  one  of  two  heads,  namely,  conductors 
and  insulators. 

Conductors  are  those  substances  offering  relatively  low 
resistance. 


THE  ELECTRICAL  CIRCUIT  7 

Insulators  are  those  substances  offering  a  high  resistance  as 
compared  to  conductors. 

There  is  no  such  thing  as  a  perfect  conductor  or  a  perfect 
insulator,  but  conductors  and  insulators  are  merely  relative 
terms  and  define  the  degree  to  which  a  substance  conducts. 
Metals  have  by  far  the  least  resistance  of  any  substances 
and  are  used  in  electrical  circuits  where  a  minimum  resist- 
ance is  desired.  The  most  common  insulators  in  use  are 
porcelain,  glass,  mica,  stoneware,  slate,  marble,  rubber,  oils, 
paraffin,  shellac,  paper,  silk,  cotton,  etc. 

The  unit  in  which  resistance  is  measured  is  the  ohm,  and 
it  is  represented  by  the  symbol  (R). 

8.  Electromotive  Force. — As  every  part  of  the  circuit  offers 
resistance   to   the   flow    of   electricity,   there   must   be   some 
force,  or  pressure,  to  overcome  this  resistance  and  maintain 
the  current.     This   is   the   electromotive  force   or  electricity 
moving  force.     Electromotive  force,  or  e.m.f.,  as  it  is  abbre- 
viated,  can   be   generated   in   a   number   of   different   ways; 
perhaps  the  two  most  common  are  the  chemical  production 
in  a  primary  cell  and  the  mechanical  generation  by  the  proc- 
ess  of  electro-magnetic   induction   in   a   generator.     Electro- 
motive force  does  not  create  electricity,  but  simply  imparts 
energy  to  it,  as  a  mechanical  force  may  produce  motion  in 
a  body  and  as  a  result  convey  energy  to  the  body.     An  elec- 
tromotive force  may  exist  without  producing  a  current,  just 
as  a  mechanical  force  may  exist  without  producing  motion. 
The  unit  in  which   electromotive  force   is   measured   is  the 
volt. 

9.  Electromotive     Force     and     Potential     Difference. — The 
electromotive    force    in    any    circuit    is    the    total    generated 
electrical  pressure  acting  in  the  circuit,  while  the  potential 
difference   is   the    difference   in    electrical   pressure   between 
any  two  points  in  the  circuit.     The  electricity  in  its  passage 
around  the  circuit  loses  some  of  its  energy;  hence,  between 
any  two  points  in  the  circuit  there  will  be  a  difference   in 
energy  or  potential   possessed  by  the   electricity.     In   over- 
coming the  resistance  of  the  wire  between  the  points  (A)  and 
CB),  Fig.  4,  the  electricity  will  lose  some  of  its  energy  and 
will,  therefore,  have  less  potential  at  (B)  than  at  (A),  or,  in 
other  words,  there  is  a  difference  in  potential  between   (A) 
and  (B).    This  difference  in  potential  in  the  electrical  circuit 


8 


PEACTICAL  APPLIED  ELECTRICITY 


is  analogous  to  the  difference  in  pressure  between  two  points 
on  the  pipe  in  the  hydraulic  circuit.  This  potential  differ- 
ence, or  p.d.,  as  it  is  abbreviated,  is  due  to  the  current  through 
the  resistance,  for  when  the  current  stops,  the  difference  in 
potential  will  no  longer  exist.  The  potential  difference  is 
measured  in  the  same  unit  as  the  electromotive  force,  the 
volt.  The  sum  of  all  the  potential  differences  in  any  elec- 
trical circuit  is  numerically  equal  to  the  effective  e.m.f.  act- 
ing in  the  circuit.  If  two  points  can  then  be  located  on  a 
circuit  so  that  all  the  p.d.'s  around  the  circuit  will  be  be- 
tween them,  the  potential  difference  between  the  points  and 
the  e.m.f.  acting  in  the  circuit  will  be  numerically  equal. 


Generator 


Fig.  4 

10.  Ohm's  Law. — Current,  electromotive  force,  and  resist- 
ance are  always  present  in  an  active  circuit  and  there  is  a 
simple,  but  very  important,  relation  connecting  them.  This 
relation  was  first  discovered  by  Dr.  G.  S.  Ohm  in  1827  and 
has,  as  a  result,  been  called  Ohm's  Law.  Dr.  Ohm  discovered 
by  experiment  that  the  difference  of  potential,  represented 
by  the  symbol  (E),  between  any  two  points  on  a  conductor, 
is,  all  other  conditions  remaining  constant,  strictly  propor- 
tional to  the  current  (I),  or 


E  =  Constant   X  I 


(2) 


By  measuring  (E)  in  volts  and  (I)  in  amperes,  the  constant  in 
the  above  equation  is  numerically  equal  to  the  resistance,  be- 
tween the  points,  in  ohms.  The  expression  can  then  be  re- 
duced to  the  form 


Volts  =  Resistance  X  Amperes 
E  =  RI 


(3) 


THE  ELECTRICAL  CIRCUIT  9 

or,  as  it  is  usually  written, 

Amperes  =  Volts  -f-  Ohms 

E 

I  =  -  (4) 

R 

and  as  a  third  form, 

Ohms  =  Volts  -5-  Amperes 
E 

R  =  (5) 

I 

The  above  relations  hold  true  for  all  or  any  part  of  a  cir- 
cuit composed  of  metals  and  electrolytes,  but  it  does  not 
seem  to  be  true  for  gases,  under  certain  conditions,  nor  for 
insulators. 

Example. — The  total  resistance  of  a  certain  circuit  is  55 
ohms.  What  current  will  a  pressure  of  110  volts  produce  in 
the  circuit? 

Solution. — The  value  of  the  current  is  given  in  terms  of 
the  pressure  and  the  resistance  in  equation  (4)  and  by  a 
direct  substitution  in  this  equation  we  have 

110 
I  =  =  2 

55 

Ans.     2  amperes. 

Example. — A  current  of  10  amperes  is  produced  in  a  circuit 
whose  resistance  is  12%  ohms.  What  pressure  is  required? 

Solution. — The  electrical  pressure  is  given  in  terms  of  the 
resistance  and  the  current  in  equation  (3)  and  by  a  direct 
substitution  in  this  equation  we  have 

E  =  12V2   X  10  =  125 

Ans.    125  volts. 

11.  Coulomb,  Ampere,  Ohm,  and  Volt. — The  International 
Electrical  Congress  that  met  in  Chicago  in  1893  officially 
passed  upon  the  following  values  for  the  coulomb,  ampere, 
ohm,  and  volt,  and  they  are  known  as  the  practical  units. 

(a)  In  defining  the  coulomb  advantage  is  taken  of  the 
fact  that  electricity  in  passing  through  a  solution  of  silver 
nitrate  deposits  silver  on  one  of  the  conductors  immersed 


10  PRACTICAL  APPLIED  ELECTRICITY 

in  the  solution  and  the  amount  deposited  is  proportional  to 
the  quantity  of  electricity  that  passed  through  the  solution. 
(See  chapter  on  "Instruments.")  The  coulomb  will  deposit, 
under  standard  conditions,  .001 118  of  a  gram  of  silver. 

(b)  Since  the   current  is  the  rate  of  flow  of  electricity, 
then  the  ampere  is  the  unit  rate  of  flow,  or  one  coulomb 
per  second,  and  its  value  is,  therefore,  that   current  which 
will  deposit  silver  at  the  rate  of  .001118  of  a  gram  per  sec- 
ond.    When  smaller  currents  are  to  be  measured,  the  mi  Mi- 
ampere,    or    one-thousandth    of    an    ampere,    and    the    micro- 
ampere, or  one-millionth  of  an  ampere,  are  frequently  used. 

(c)  The    International   ohm,   as   nearly   as   known,   is   the 
resistance  of  a  uniform  column  of  pure  mercury  106.3  centi- 
meters long  and  14.4521  grams  in  mass,  at  the  temperature 
of   melting   ice.      This    makes    the    cross-section    one    square 
millimeter.     The   microhm   is   one-millionth   of  an  ohm   and 
the  megohm  is  one  million  ohms.     These  units  are  very  fre- 
quently used  in  the  measurement  of  very  small  or  very  large 
resistances. 

(d)  The   volt,   the  unit  of  electromotive  force   or   poten- 
tial difference,  is  that  e.m.f.  or  p.d.  which,  when  applied  to 
a  conductor  having  a  resistance  of  one  ohm,  will  produce  in 
it  a  current  of  one  ampere.    One  volt  equals  the  1009l434  part 
of  the  e.m.f.  of  a  Clark  Standard   Cell  at  15  degrees  centi- 
grade.   A  smaller  unit,  called  the  millivolt,  or  one-thousandth 
of  a  volt,  is  often  used  in  measuring  small  e.m.f.'s  and  p.d.'s. 
Another  unit,  called  the  kilovolt,  has  a  value  of  one  thousand 
volts. 

PROBLEMS    ON    OHM'S    LAW 

(1)  The  difference  in  potential  between  the  terminals  of 
a  generator  is  110  volts.     If  the  generator  is  causing  a  cur- 
rent of  12  amperes  in  the  circuit  to  which  it  is  connected, 
what  is  the  resistance  of  the  circuit? 

Ans.    9.17  ohms. 

(2)  What  e.m.f.   must  a  dynamo   generate  to  supply  an 
electroplating  current  of  20  amperes  through  a  circuit  whose 
total  resistance  is  .2  ohms?  Ans.    4  volts. 

(3)  An  electric-car  heater  is  supplied  with  a  p.d.  of  500 


THE  ELECTRICAL  CIRCUIT  U 

volts  from  the  trolley.     What  must  its  resistance  be  in  or- 
der that  the  current  may  not  exceed  8  amperes? 

Ans.     62.5  ohms. 

(4)  The  difference  in  potential  between  the  terminals  of 
an  incandescent  lamp   is   110   volts   when   there  is   a  direct 
current   of   .5   ampere   through   the   lamp.     What  is   the   re- 
sistance of  the  lamp?  Ans.    220  ohms. 

(5)  The  field  circuit  of  a  dynamo  takes  a  current  of  1.5 
amperes  from  a  110-volt  circuit.     What  is  the  resistance  of 
the  field  winding?  Ans.    73%  ohms. 

(6)  A   certain  bell  requires  a  p.d.  at  its  terminals  of   8 
volts  to  operate  it.     The  bell  has  a  resistance  of  50  ohms. 
What  current  is  required  to  operate  the  bell? 

Ans.     .16  ampere. 

(7)  An  e.m.f.  of  5  volts  is  connected  to  a  line  and  bell 
having  a  combined  resistance  of  12y2  ohms.     What  current 
is  there  through  the  bell?  Ans.    .4  ampere. 

(8)  A  lamp  has  a  hot  resistance  of  55  ohms  and  requires 
a  current  of  1  ampere  to  cause  it  to  light  up  to  full  candle- 
power.     What  p.d.  must  exist  between  the  terminals  of  the 
lamp  when  it  burns  at  full  candle-power? 

Ans.    55  volts. 

12.  Electrical  Force. — Force  is  defined  as  that  which 
tends  to  produce  motion,  or  a  change  of  motion;  thus  a  force 
must  always  be  applied  to  a  body  to  cause  it  to  move,  and 
a  force  must  be  again  applied  to  cause  the  body  to  come 
to  rest.  It  must  be  remembered  that  a  force  does  not  al- 
ways produce  motion,  but  only  tends  to  produce  it,  as  when 
you  push  on  a  brick  wall  you  apply  muscular  force,  but  there 
is  no  motion.  There  are  a  number  of  different,  kinds  of 
force:  Gravitational  force,  as  a  result  of  which  all  bodies  fall 
from  a  higher  to  a  lower  level:  mechanical  force,  which  is 
produced  by  the  expansion  of  the  steam  in  the  engine  cylin- 
der, and  may  be  used  in  driving  a  generator;  and  electrical 
force  is  that  force  which  produces  or  tends  to  produce  a 
movement  of  electricity.  It  is  commonly  produced  in  the  pri- 
mary battery  or  by  an  electrical  generator. 


12  PEACTICAL  APPLIED  ELECTRICITY 

13.  Electrical  Work  or  Energy.— When  a  force  overcomes 
a  certain  resistance,  work  is  done;  or  work  is  the  result  of 
a  force  acting  through  a  certain  distance.  Force  may  exist 
without  any  work  being  done.  Thus,  a  generator  may  be  op- 
erating and  generating  an  electrical  force,  but  it  is  not 
sufficient  to  overcome  the  resistance  between  the  terminals 
of  the  machine,  therefore,  no  current  is  produced  and  the 
generator  is  not  doing  any  work.  If,  however,  a  conductor 
be  connected  to  the  terminals  of  the  generator,  a  current 
will  be  produced  and  as  a  result  the  generator  will  do  work. 
The  electrical  work  done  by  the  dynamo  will  show  itself 
as  heat  and  the  wire  will  become  heated  as  a  result.  En- 
ergy is  the  ability  to  do  work.  Electrical  energy,  then,  is 
the  capacity  or  ability  to  do  electrical  work.  Energy  is 
measured  in  the  same  unit  as  work  and  it  is  numerically 
equal  to  the  work  done.  Thus  the  energy  possessed  by  a 
certain  quantity  of  electricity,  with  respect  to  its  energy  at 
some  other  electrical  level,  is  equal  to  the  work  done  on  or 
by  the  quantity  in  moving  from  the  first  to  the  second 
electrical  level.  When  a  quantity  moves  from  a  higher  to 
a  lower  level,  it  gives  up  energy  or  does  work;  when  it  is 
moved  from  a  lower  to  a  higher  electrical  level,  work  is 
performed  and  the  energy  of  the  quantity  of  electricity  is 
increased. 

14. — The  Joule. — The  joule,  the  unit  of  electrical  work 
or  energy,  is  the  amount  of  work  performed  in  raising  one 
coulomb  of  electricity  through  a  difference  in  electrical 
pressure  of  one  volt.  Work  is  independent  of  the  time. 
In  other  words,  it  will  require  the  same  amount  of  work 
to  raise  a  certain  weight  a  given  height  in  one  hour  as 
would  be  required  to  raise  it  the  same  height  in  one  minute. 
The  name  for  the  mechanical  unit  of  work  is  a  compound 
word  in  which  one  of  the  parts  is  a  force  unit  and  the  other 
part  is  a  distance  unit.  The  unit  commonly  used  is  the  foot- 
pound, the  pound  being  the  unit  of  force  and  the  foot  the  unit 
of  distance.  The  electrical  work  performed  in  an  electrical 
circuit  is  equal  to 

Joules  =  Volts  X  Amperes  X  Time  (in  seconds)     (6) 

Amperes  times  time  is  equal  to  the  quantity  of  electricity 
moved,  so  that  the  right-hand  portion  of  the  above  equation 


THE  ELECTKICAL  CIECUIT  13 

is  the  product  of  a  certain  quantity  and  the  difference  in 
electrical  pressure  through  which  it  is  moved. 

15.  Electrical  Power. — Power  is  the  rate  of  doing  work, 
or  the  rate  at  which  energy  is  expended.  The  unit  of  elec- 
trical power  is  a  unit  of  electrical  work  performed  in  a  unit 
of  time,  or  a  joule  per  second,  and  it  is  called  the  watt,  rep- 
resented by  the  symbol  (W). 

Electrical  Work 

Electrical  Power= (7) 

Time 

Substituting  the  value  of  the  electrical  work  given  in  equa- 
tion (6)  in  equation  (7)-,  we  have 

Volts  X  Amperes  X  Time 

Electrical  Power  = 

Time 

=  Volts  X  Amperes,  or  (8) 

W  =  El  (9) 

One  watt,  therefore,  equals  one  volt  multiplied  by  one  am- 
pere, or  any  product  of  volts  and  amperes  whose  result  is 
unity.  Equation  (9)  may  be  written 

W 

I  =  (10) 

or  E 

W 

E= (11) 

I 

Example. — A  220-volt   generator  supplies  20  amperes  to  a 
motor.     How  many  watts  does  the  motor  consume? 
Solution.— Substituting  directly  in  equation  (9)  we  have 

W  =  220  X  20  =  4400 

Ans.     4400  watts. 

Example.— An  arc  lamp  requires  880  watts  from  a  110-volt 
circuit  to  operate  it.     What  current  does  the  lamp  take? 
Solution.— Substituting  in  equation  (10)  we  have 


14  PRACTICAL  APPLIED  ELECTRICITY 

880 

I  =  =  8 

110 

Ans.     8   amperes. 

16.  Mechanical    Horse-Power. — If   a    body   weighing   33000 
pounds  be  raised  one  foot  in  one  minute,  there  is  a  rate  of 
working,  or  expenditure  of  energy,  equivalent  to  one  horse- 
power   (abbreviated    h.p.).     The    horse-power    any    machine 
is  developing  is  equal  to  the  foot-pounds  of  work  done  per 
minute  divided  by  33  000,  or  the  foot-pounds  of  work  done 
per  second  divided  by  550. 

17.  Relation   between  the   Watt  and  the   Foot-Pound.— Dr. 
Joule  discovered  experimentally  that 

One  watt  =  .7375  foot-pound  per  second          (12) 
or 

One  foot-pound  per  second  =  1.356  watts       (13) 

18.  Electrical    Horse-Power. — Since  the  mechanical  horse- 
power is  550  foot-pounds  per  second,  an  equivalent  rate  of 
doing  work  would  be 

550 

=  746   watts  =  1   electrical   horse-power       (14) 

.7375 

Then   to   change   from   mechanical   horse-power  to   the   elec- 
trical units,  multiply  by  746,  or 

Watts  =  h.p.  X  746  (15) 

To  determine  the  horse-power  a  generator  is  developing,  de- 
termine its  output  in  watts  and  divide  by  746,  or 

E  X  I        watts 

hp.= = (16) 

746  746 

19.  Kilowatt. — The  kilowatt  (abbreviated  k.w.)  is  a  larger 
unit  of  electrical  power  than  the  horse-power.     It  is  equal 
to  1000  watts  or  about  1%  horse-power. 

20.  Larger   Units  of   Energy. — The   joule  is  a  very   small 
unit  of   electrical   energy   or   work,    and   as   a   result   larger 


THE  ELECTK1CAL  CIRCUIT  15 

units  are  usually  used  in  practice.  The  watt-hour  is  one 
watt  expended  for  one  hour.  The  kilowatt-hour  is  equal  to 
1000  watts  expended  for  one  hour.  The  watt-hour  is  equiva- 
lent to  3600  watt-seconds  or  60  watt-minutes. 

Watt-hours  =  watts  X  hours  (17) 

Kilowatt-hours  =  k.w.  X  hours  (18) 

Horse-power  hour  =  h.p.  X  hours  (19) 

The  dials  of  the  integrating  wattmeters  used  by  central 
station  companies  usually  record  the  energy  supplied  to  the 
consumer  for  lighting  or  power  purposes  in  watt-hours  or 
kilowatt-hours. 

Example.  —  Ten  incandescent  lamps  take  a  current  of  21X> 
amperes  from  a  220-volt  circuit.  What  will  it  cost  to  operate 
these  lamps  .  for  five  hours  if  the  power  company  charges 
14  cents  per  kilowatt-hour? 

Solution.  —  Substituting  in  equation  (9),  we  can  determine 
the  power  taken  by  the  lamps  in  watts: 

Power  =  220   X   2%  =  550  watts 

Now  by  substituting  in  equation  (17),  we  can  determine  the 
energy  consumed  in  watt-hours 

Energy  =  550  X  5  =  2750  watt-hours 

One  kilowatt-hour  is  equivalent  to  1000  watt-hours,  hence  2750 
watt-hours  are  equal  to  2.75  kilowatt-hours.  The  total  cost 
then  would  be 

2.75  X  14  =  38% 

38%  cents. 


21.  Units.  —  Units  are  of  two  kinds  —  fundamental  and  de- 
rived. The  fundamental  units  are  the  ones  from  which  all 
others  are  derived  and  in  terms  of  which  all  physical  meas- 
urements may  be  made.  They  are  fundamental  in  the  sense 
that  no  one  is  derived  from  the  others.  The  derived  units 
are  all  those  that  are  dependent  for  their  definition  upon  the 
fundamental  ones. 

The  three  fundamental  units  in  use  are  those  of  length, 
mass,  and  time.  Of  these  the  only  unfamiliar  one  may  be 


16 


PEACTICAL  APPLIED  ELECTKICITY 


that  of  mass,  which  means  the  quantity  of  matter  in  a 
body.  From  these  three  fundamental  units  are  derived  all 
others  in  use,  such,  for  example,  as  those  of  force,  work, 
and  energy  already  mentioned,  and  all  of  the  electrical  units. 

22.  Systems  of  Units. — Unfortunately  there  are  two  sys- 
tems of  units  in  use  in  this  country.  One  is  the  ordinary 
commercial,  or  English  System,  and  the  other  the  universal 
scientific,  or  Metric  System.  In  each  of  these  systems  we 
have  the  three  fundamental  units  and  also  a  set  of  derived 
units.  It  is  quite  essential  that  you  know  something  of 
the  metric  system,  since  all  the  electrical  units  are  based 
upon  it,  and  a  great  many  dimensions  will  be  given  in  units 
that  belong  to  this  system.  Table  No.  I  will  show  the  most 
common  units  in  the  two  systems. 

The  English  System  is  sometimes  spoken  of  as  the  foot- 
pound-second (f.p.s.)  system,  because  of  the  three  funda- 
mental units  upon  which  it  is  based.  Similarly  the  Metric 
System  is  frequently  spoken  of  as  the  centimeter-gram-sec- 
ond  (c.g.s.)  system. 

The  relation  between  the  units  of  the  two  systems  is  given 
in  Table  A,  Chapter  20. 

TABLE  NO.  I 


RELATION  OP  UNITS   IN  ENGLISH  AND  METRIC    SYSTEMS 


UNITS 

SYSTEM 

LENGTH 

MASS 

TIME 

English  or 
(F,  P.  S.) 

Yard  (yd.) 
Foot    (ft.) 

Pound  (Ib.) 
Ounce  (oz.) 

Second  (sec.) 

Metric  or 
(C.  G.  S.) 

Meter  (m.) 
Centimeter  (cm.) 

Kilogram  (kg.) 
Gram  (g.) 

Second  (sec.) 

PROBLEMS    ON    POWER    AND    ENERGY    CALCULATIONS 

(1)     If  4000  watts  are  expended  in  a  circuit,  how  many 
horse-power  are  being  developed? 

Ans.    5.36-1-  horse-power. 


THE  ELECTKICAL  CIRCUIT  17 

(2)  If  20  horse-power  of  mechanical  energy  were  converted 
into  electrical  energy,  how  many  watts  would  be  developed? 

Ans.     14  920  watts. 

(3)  One   hundred   and   twenty-five   horse-power   expended 
continuously  for  one  hour  will  produce  how  many  kilowatt- 
hours?  Ans.     93.25  k.w.-hours. 

(4)  How    many    watts    are    expended    in    a    110-volt,    16- 
candle-power  lamp  that  requires  a  current  of  .5  ampere? 

Ans.     55  watts. 

(5)  How  many  horse-power  will  be  absorbed  by  a  circuit 
of  series   arc    lamps   taking   9.6    amperes,   the   line   pressure 
being  2000  volts  Ans.     25.73  +  horse-power. 

(6)  A  motor  takes  a  current  of  5  amperes  from  a   110- 
volt  circuit.     What  will  it  cost  to  operate  this  motor  for  10 
hours,  if  the  central  station  company  charges  12  cents  per 
kilowatt-hour?  Ans.     66  cents. 


CHAPTER  II 

CALCULATION  OF  RESISTANCE 

23.  Resistance. — Resistance  has   been   defined   as   a   prop- 
erty of  materials  which  opposes  the  free  flow  of  electricity 
through  them.    The  value  of  the  resistance  of  any  conductor 
in  ohms  will,  however,  depend  upon  the  dimensions,  tempera- 
ture, and  the  kind  of  material  of  which  it  is  composed. 

24.  Conductance. — The  inverse  of  resistance  is  known  as 
the   conductance   of   a   conductor.     That   is,   if   a    conductor 
has  a  resistance  of    (R)   ohms,  its  conductance  .is   equal   to 
(14-R).    The  unit  in  which  the  conductance  is  measured  is 
the  mho,  and  it  is  the  conductance  offered  by  a  column  of  pure 
mercury   106.3   cm.  long  and   14.4521   grams   in  mass   at  the 
temperature  of  melting  ice.     This  unit  is  little  used  in 'prac- 
tice except  in  the  calculation  of  the  resistance  of  a  divided 
circuit,  which  will  be  taken  up  later. 

25.  Resistance    Varies    Directly  as   the    Length    of   a   Con- 
ductor.— The   resistance    of   a    conductor    is    directly    propor- 
tional to  its  length,  the  temperature  and  cross-section  of  the 
conductor   remaining   constant.     That    is,    the   resistance    in- 
creases  at  the   same   rate   the   length   of  the   conductor   in- 
creases, just  as  the  resistance  of  a  pipe  to  the  flow  of  wa- 
ter   increases    as    the    length    of   the    pipe    is    increased,    all 
other   conditions   remaining  constant.     Hence,   if  the   length 
of  a  conductor  is  increased  to  four  times  its  original  value, 
the  resistance  will  be  four  times  as  much;   or  if  the  length 
is  divided  into  four  equal  parts,  the  resistance  of  each  part 
will  be  one-fourth  of  the  total  resistance. 

Example. — The  resistance  of  a  piece  of  wire  fifteen  feet 
long  is  5  ohms.  What  is  the  resistance  of  1000  feet  of  the 
same  kind  of  wire? 

18 


CALCULATION  OF  RESISTANCE  19 

Solution. — Since  the  resistance  of  a  conductor  is  directly 
proportional  to  its  length,  we  can  determine  the  resistance 
of  one  foot  of  the  wire,  knowing  the  resistance  of  five  feet, 
by  dividing  5  by  15: 

5  -r- 15  =  y3 

The  resistance  of  one  foot,  then,  is  %  ohm,  and  the  resist- 
ance of  1000  feet  would  be  1000  times  as  much,  or 
1000  X  %  =  333% 

Ans.     333 y3   ohms. 

Example. — The  resistance  of  a  certain  conductor  thirty 
feet  long  is  30  ohms.  What  is  the  resistance  of  three  inches 
of  the  conductor? 

Solution. — The  length  of  the  conductor  in  inches  is  equal 
to  the  number  of  inches  per  foot  (12)  multiplied  by  the  num- 
ber of  feet: 

12  X  30  =  360 

Since  the  length  is  360  inches  and  the  resistance  is  30  ohms, 
the  resistance  per  inch  can  be  obtained  by  dividing  30  by 
360: 

30  -r-  360  =  i/i2 

The  resistance  of  one  inch  is  then  i£2  ohm  and  the  resist- 
ance of  three  inches  will  be  three  times  one-twelfth: 

3  X  Ii2  -  3/i2  =  % 

Ans.     ^4  ohm. 

26.  Resistance  Varies  Inversely  as  the  Cross-Section  of  a 
Conductor. — The  resistance  of  a  conductor  is  inversely  pro- 
portional to  the  cross-section,  the  temperature  and  length 
of  the  conductor  remaining  constant.  That  is,  the  resist- 
ance decreases  at  the  same  rate  the  area  of  the  cross-sec- 
tion increases,  all  other  quantities  remaining  constant. 
Hence,  if  the  area  of  a  conductor  is  reduced  to  one-fourth 
its  original  value,  the  resistance  will  be  four  times  as  much, 
or  if  its  area  is  increased  to  four  times  its  previous  value 
the  resistance  will  be  decreased  to  one-fourth  its  original 
value. 

Example. — A  conductor  %00  square  inch  in  area  has  a 
resistance  of  .075  ohm  per  foot.  What  is  the  resistance 
of  a  conductor  of  the  same  material  }£5  of  a  square  inch 
in  area  and  one  foot  long? 


20  PRACTICAL  APPLIED  ELECTKICITY 

Solution. — Since  the  resistance  varies  inversely  as  the  re- 
lation between  the  areas,  and  the  relation  between  the  areas 
in  this  case  is 

%5  -*•  a/ioo  =  4 

the  resistance  of  the  conductor  of  larger  cross-section  will 
be  %  the  resistance  of  the  conductor  of  smaller  cross- 
section. 

%  of  .075  =  .018  75 

Ans.     .018  75  ohm. 

27.  Area  of  Circular  Conductors. — Most  all  conductors 
have  a  circular  cross-section;  and  it  is  necessary  to  know 
how  to  calculate  their  areas  in  terms  of  their  diameters  or 
radii  in  order  to  determine  the  relation  between  their  re- 
sistances. The  area  of  any  circle  is  obtained  by  multiplying 
the  radius  by  itself  and  this  product  by  a  constant  called 
Pi.  The  value  of  this  constant  is  3.1416,  and  it  is  the  num- 
ber of  times  the  diameter  must  be  used  in  order  to  reach 
around  the  circle.  It  is  represented  by  the  Greek  symbol  (TT). 
Hence,  the  area  of  any  circle  can  be  obtained  by  using  the 
equation 

Area  =  r2  x  TT  (20) 

Area  =  radius  X  radius  X  pi 

Since  the  diameter  of  a  circle  is  equal  to  twice  the  radius, 
this  equation  may  be  rewritten  in  terms  of  the  diameter, 

Area  =  (j)2  X  *• 

7T 

Area  =  —  X  d2 

4 
Area  =  .7854  d3  (21) 

From  the  above  equation  it  is  seen  that  the  area  of  one 
circle  bears  the  same  relation  to  the  area  of  another  as  exists 
between  their  respective  diameters  squared.  That  is,  if  two 
circles  have  diameters  3  and  5,  the  relation  between  their 
areas  will  be  the  relation  between  (3)2  and  (5)2,  or  9  and  25. 
The  circle  of  smaller  diameter  will  have  %5  the  area  of 
the  circle  of  larger  diameter. 

Example. — The  resistance  of  a  wire  .1  inch  in  diameter  and 


CALCULATION  OF  RESISTANCE  21 

10  feet  long  is  10  ohms.     What  is  the  resistance  of  a  wire 
of  the  same  material  and  same  length  .3  inch  in  diameter? 

Solution. — The  ratio  of  the  areas  of  the  two  wires  will  be 
the  ratio  between  .I2  and  .32  which  is  .01  and  .09.  The  larger 
wire  will  have  9  times  the  area  of  the  smaller  wire  and  since 
the  resistance  varies  inversely  as  the  area  it  will  have  one- 
ninth  the  resistance. 

1/9  of   10  =  19/9  =  11/9 

Ans.     1%  ohms. 

28.  Resistance   Changes  with   Temperature. — A  change  in 
the  temperature  of  all  substances  will  cause  a  change  in  their 
resistance.    In  the  majority  of  cases  an  increase  in  tempera- 
ture means  an  increase   in  resistance.     Carbon  is  the  best 
example  of  substances  whose  resistance  decreases   with  an 
increase  in  temperature.     The  resistance  of  the  carbon  fila- 
ment of  an  incandescent  lamp  is  about  twice  as  great  when 
the  lamp  is  cold  as  when  it  is  lighted.    The  change  in  resist- 
ance due  to  a  change  in  temperature  is  quite  different  for 
different  materials,  and  it  is  also  slightly  different  for  the 
same  materials  at  different  temperatures.     Alloys,   such   as 
manganin,  have  a  very  small  chance  in  resistance  due  to  a 
change   in  temperature,   and   standard  resistances   are,   as  a 
rule,  made  from  such  alloys,  as  it  is  desired  to  have  their 
resistance  remain  as  near  constant  as  possible. 

29.  Temperature   Coefficient. — The  temperature   coefficient 
of  a  material  is  defined  as  the  change  in  resistance  per  ohm 
due  to  a  change  in  temperature  of  one  degree.    The  resistance 
at  0°   centigrade  or  32°  Fahrenheit  is  usually  taken  as  the 
standard    resistance,   which   we   will   call   R0.     Now,    let   the 
resistance  at  some  higher  temperature  (t)  be  measured  and 
call  it  Rt.     Then  R0  —  Rt  is  the  change  in  resistance  for  a 

Rt  — Ro 
change   in  temperature  of    (t)    degrees,   and  —  is  the 

Ro 

change  in  resistance  per  ohm  for  the  given  change  in  tem- 
perature (t).    The  change  in  resistance  for  each  ohm  due  to 
a  change  in  temperature  of  one  degree  is 
Rt  —  Ro 

-  =  a  (22) 

Rot 


22  PBACTICAL  APPLIED  ELECTRICITY 

in  which  (a)  is  the  temperature  coefficient.  When  the  re- 
sistance increases  with  an  increase  in  temperature,  as  in 
the  case  of  metals,  then  Rt  is  greater  than  R0  and  (a)  is 
positive;  if  Rt  decreases  with  a  rise  of  temperature,  as  in 
the  case  of  carbon,  then  (a)  is  negative.  The  above  ex- 
pression for  the  temperature  coefficient  can  be  changed  to 
the  form 

Rt  =  R0   (i  4-  at)  (23) 

This  equation  gives  the  value  of  the  resistance  (Rt)  at  any 
temperature  (t)  in  terms  of  the  resistance  (R0)  the  tempera- 
ture coefficient  (a),  and  the  change  in  temperature  (t). 

30.  Values  of  Temperature  Coefficients. — Table  No.  II  gives 
the  value  of  the  temperature  coefficient  for  a  number  of 
materials  when  the  temperature  change  is  expressed  in  centi- 
grade (ac)  and  Fahrenheit  (af)  degrees. 


TABLE  NO.  II 
TEMPERATURE    COEFFICIENTS 

Material  ac  at 

Aluminum     0.004  35  0.002  417 

Carbon     0.0003  0.00017 

Copper     0.004  20  0.002  33 

Iron    0.00453  0.00252 

Lead    (pure) 0.004  11  0.002  2 

Mercury    0.00088  0.00049 

Nickel    0.00622  0.00345 

Platinum  0.002  47  0.001  37 

Silver     0.003  77  0.002  1 

Tin    0.004  2  0.002  3 

Zinc    (pure) 0.004  0.002  2 

The  relation  between  the  two  coefficients  as  given  in  the 
table  is  the  same  as  that  between  the  centigrade  and  the 
Fahrenheit  degree;  that  is  at  =  %  ac. 

Table  B,  Chapter  20,  gives  the  relation  between  the  cen- 
tigrade and  Fahrenheit  thermometer  scales. 

The  above  values  of  the  temperature  coefficients  are  based 
upon  a  change  in  resistance,  due  to  a  change  in  temperature 


CALCULATION  OF  RESISTANCE  23 

from  0°  centigrade  or  32°  Fahrenheit.  If  the  original  tem- 
perature of  the  conductor  is  not  0°  centigrade  or  32°  Fahren- 
heit, the  value  of  the  temperature  coefficient  will  not  be  the 
same  as  that  given  in  Table  No.  II.  There  will  be  a  different 
value  obtained  for  (a)  for  each  different  initial  temperature. 
Table  No.  Ill  gives  the  change  in  the  value  of  (a)  for  copper 
for  initial  temperatures  from  0°  to  50°  centigrade. 


TABLE  NO.  Ill 


VALUES  OP 

THE  TEMPERATURE  COEFFICIENT  OF  COPPER  AT 

DIFFERENT   INITIAL 

TEMPERATURES 

CENTIGRADE 

Initial 

Temp,  coefficient 

Initial 

Temp,  coefficient 

temperature 
deg.  Cent. 

per 
deg.  Cent. 

temperature 
deg.  Cent. 

per 
deg.  Cent. 

0 

.004  200 

26 

.003  786 

1 

.004  182 

27 

.003  772 

2 

.004  165 

28 

.003  758 

3 

.004  148 

29 

.003  744 

4 

.004  131 

30 

.003  730 

5 

.004  114 

31 

.003  716 

6 

.004  097 

32 

.003  702 

7 

.004  080 

33 

.003  689 

8 

.004  063 

34 

.003  675 

9 

.004  047 

35 

.003  662 

10 

.004  031 

36 

.003  648 

11 

.004015 

37 

.003  635 

12 

.003  999 

38 

.003  622 

13 

.003  983 

39 

.003  609 

14 

.003  967 

40 

.003  596 

15 

.003  951 

41 

.003  583 

16 

.003  936 

42 

.003  570 

17 

.003  920 

43 

.003  557 

18 

.003  905 

44 

.003  545 

19 

.003  890 

45 

.003  532 

20 

.003  875 

46 

.003  520 

21 

.003  860 

47 

.003  508 

22 

.003.845 

48 

.003  495 

23 

.003  830 

49 

.003  483 

24 

.003  815 

50 

.003  471 

25 

.003  801 

24  PRACTICAL  APPLIED  ELECTRICITY 

31.  Calculation  of  Resistance  Due  to  Change  in  Tempera- 
ture. —  When  the  resistance  of  a  conductor  at  a  given  tem- 
perature is  known,  which  we  will  assume  is  0°  centigrade, 
its  resistance  at  some  other  temperature  may  be  calculated 
by  the  use  of  the  temperature  coefficient.  If  it  is  desired 
to  calculate  the  resistance  of  a  conductor  at  a  higher  tem- 
perature than  that  at  which  it  was  measured,  proceed  as 
follows:  Multiply  the  temperature  coefficient  by  the  change 
in  temperature  and  the  product  will  be  the  change  in 
resistance  of  each  ohm  for  the  given  change  in  tempera- 
ture; multiplying  this  product  by  the  original  resistance  in 
ohms  gives  the  total  change  in  resistance  of  the  conductor. 
This  increase  in  resistance  must  now  be  added  to  the  original 
value  and  the  result  is  the  resistance  at  the  second 
temperature. 

The  method  just  given  for  calculating  the  resistance  with 
a  change  in  temperature  can  be  expressed  by  the  following 
equation  : 

(24) 


or,  it  is  usually  written 

Rt  =  Ro   (1  +  at)  (25) 

In  the  above  equation  (Rt)  is  the  resistance  at  the  second 
temperature,  (R0)  the  resistance  at  the  first  temperature, 
(0°  centigrade),  (a)  the  temperature  coefficient,  and  (t)  the 
number  of  degrees  above  or  below  freezing  (0°  centigrade  or 
32°  Fahrenheit). 

The  value  of  (a)  to  use  in  the  equation  will  depend  upon 
whether  the  change  in  temperature  (t)  is  to  be  measured 
on  the  centigrade  or  on  the  Fahrenheit  scale. 

By  an  inspection  of  equation  (25)  it  is  apparent  that  if  the 
resistance  of  a  conductor  at  a  higher  temperature  is  known, 
the  resistance  at  a  lower  temperature  can  be  calculated  from 
the  equation 

Rt 

R0  =  -  (26) 

1  +  at 

When  the  resistance  of  a  conductor  at  two  different  tem- 
peratures is  known,  the  change  in  temperature  can  be  calcu- 
lated from  the  equation 


CALCULATION  OF  RESISTANCE  25 

Rt  — Ro 

/97V 

\"*  ) 

R0a 

Practical  use  is  made  of  this  equation  in  what  is  known 
as  the  resistance  thermometer,  where  the  change  in  resist- 
ance of  a  coil  of  wire  is  measured  and  the  change  in  tem- 
perature calculated.  (R0)  is  then  the  resistance  of  the  coil 
at  a  known  temperature  (T0),  and  (Rt)  is  the  resistance  of 
the  coil  at  some  other  temperature  (T^.  (TJ  is  then 
equal  to 

T!  =  To  +  t  (28) 

If  there  is  an  increase  in  resistance,  (t)  is  positive  and  if 
there  is  a  decrease,  (t)  is  negative.  Hence  (Tx)  will  be 
greater  or  less  than  (T0)  depending  upon  the  sign  of  (t). 

Example. — The  resistance  of  a  certain  copper  conductor 
is  15  ohms  at  0°  centigrade.  What  is  its  resistance  at  50° 
centigrade? 

Solution. — The  temperature  coefficient  for  copper,  when  the 
temperature  is  measured  on  the  centigrade  scale,  is,  from 
Table  No.  II,  found  to  be  .0042.  Substituting  the  values  for 
(R0),  (a),  and  (t)  in  equation  (25),  we  have 

Rt  =  15  (1  +  .0042  X  50)  =18.15 

Ans.     18.15  ohms. 

Example. — The  resistance  of  a  silver  wire  is  25  ohms  at 
45°  Fahrenheit.  What  resistance  will  it  have  at  32°  Fah- 
renheit? 

Solution. — The  temperature  coefficient  for  silver  is  found 
from  Table  No.  II  to  be  .0021.  Substituting  the  values  for  (a), 
(t),  which  is  (45  —  32  =  13),  and  (Rt)  in  equation  (26),  we  have 

25  25 

Ro  =  -  -  =  24.33 

1  +  13  X  .0021        1.0273 

Ans.     24.33  ohms. 

Example. — A  certain  platinum  coil  that  is  used  'as  a  re- 
sistance thermometer  has  a  resistance  of  100  ohms  at  0° 
centigrade.  What  is  the  temperature  of  the  coil  when  its 
resistance  is  115  ohms? 

Solution. — The  temperature  coefficient  for  platinum  is  found 


26  PBACTICAL  APPLIED  ELECTRICITY 

from  Table  No.  Ill  to  be  .00247.   Substituting  the  values  of  the 
resistance  and  (a)  in  equation  (27),  we  have 

115  —  100  15 

t  =  -  -  =  60.73— 

100  X  .002  47        .247 

Since  the  original  temperature  (T0)  of  the  coil  or  the  one 
at  which  (R0)  was  determined  was  0°  centigrade,  the  final 
temperature  (TO  can  be  determined  by  substituting  the  values 
of  (T0)  and  (t)  in  equation  (28),  which  gives 

Tx  =  0  +  60.73  =  60.73— 

Ans.     60.73  —  degrees  centigrade 

All  of  the  above  calculations  are  based  on  an  initial  tem- 
perature of  0°  centigrade  or  32°  Fahrenheit.  It  is  often  the 
case  that  the  resistance  of  a  conductor  is  known  at  some 
temperature  other  than  freezing,  and  it  is  desired  to  know 
its  resistance  at  some  other  temperature.  Thus,  the  resist- 
ance of  a  certain  coil  of  wire  may  be  known  at  20°  centi- 
grade and  it  is  desired  to  know  its  resistance  at  60°  centi- 
grade. In  this  case  the  resistance  of  the  coil  at  0°  centi- 
grade should  be  determined  first,  by  the  use  of  equation 
(26),  and  the  value  of  (R0),  thus  determined,  together  with 
the  value  of  (a)  and  (t)  substituted  in  equation  (25),  which 
will  give  the  value  of  the  resistance  at  the  second  tempera- 
ture. The  above  operations  can  be  combined,  which  will 
give  the  equation 


(29) 


In  the  above  equation  (t,)  is  the  final  temperature  and  (t) 
is  the  initial  temperature,  above  or  below  freezing;  (Rt) 
the  original  resistance;  (Rt+ti)  the  final  resistance;  and  (a) 
the  temperature  coefficient.  If  the  temperatures  are  meas- 
ured on  the  Fahrenheit  scale,  the  values  of  (t)  and  (t,) 
should  be  measured  above  or  below  32°  depending  upon 
whether  the  temperature  be  above  or  below  freezing. 

Example.  —  A  coil  of  platinum  wire  has  a  resistance  of  100 


CALCULATION  OF  RESISTANCE  27 

ohms  at  45°  Fahrenheit.  What  will  the  resistance  of  this 
coil  be  at  75°  Fahrenheit? 

Solution. — This  problem  can  be  solved  by  using  equation 
(29).  The  value  of  (Rt)  to  substitute  in  the  equation  is 
100;  the  value  of  (t)  is  (45  —  32),  or  13;  the  value  of  (tj  is 
(75  —  32),  or  43;  and  the  value  of  (a)  is  .00137.  Substitut- 
ing the  above  values  in  the  equation  gives  the  value  of 
(Rt+ti),  which  is  the  value  of  the  resistance  of  the  coil  at 
(ti)  degrees  above  freezing,  or  in  this  case  75°  Fahrenheit: 

100  (1  +  .00137  X  43) 

Rt+tl  =  -  -  =  104.03  + 

(1  +  .001  37  X  13) 

Ans.     104.03-f   ohms. 

The  error  introduced,  if  the  calculation  be  made  without 
reducing  the  resistance  to  zero,  is  not  very  large,  depending 
upon  the  initial  temperature,  and  in  the  majority  of  ordinary 
cases  equation  (25)  can  be  used.  When  this  equation  is  used 
(R0)  represents  the  initial  resistance,  which  should  be  writ- 
ten (Rt);  (Rt)  represents  the  final  resistance,  which  should 
be  written  (Rt+tJ ;  and  (t)  represents  the  change  in  tempera- 
ture, which  is  equal  to  (tx —  t).  Equation  (25)  may  then  be 
rewritten  as  follows: 

Rt+tl  =  Rt  [1  +  a  a  —  t)  ]  (30) 

Using  this  equation  in  calculating  the  resistance  in  the  last 
problem  gives 

Rt+tl  =  100  [1  +  .001  37  (75  —  43)  ] 
=  100  (1  +  .0411) 
=  104.11 

Ans.     104.11  ohms. 

Equation  (29)  must  then  be  used  when  an  accurate  determi- 
nation of  the  resistance  is  desired.  Equation  (29)  can  be 
rewritten  so  that  the  value  of  (tj  can  be  calculated  when 
the  proper  substitution  is  made: 

[Rt+tlCl  +  at)]— Rt 

tx  = (31) 

aRt 

32.     Relation  of  Resistance  to  Physical   Dimensions. — From 

section  (26)  we  know  the  resistance  varies  directly  as  the 
length,  and  from  section  (27)  inversely  as  the  area  of  the 


£8  PRACTICAL  APPLIED  ELECTRICITY 

cross-section.     These  two  relations  may  be  combined  with  a 
constant,  giving  the  following  equation: 

I 
R  =  K—  (32) 

A 
The  above  equation  expresses  three  facts: 

(a)  The  resistance  (R)  varies  directly  as  the  length  (I)  of 
the  conductor. 

(b)  The  resistance  varies  inversely  as  the  cross-sectional 
area  (A)  of  the  conductor. 

(c)  The   resistance  depends  upon  the  material  of  which 
the  conductor  is  composed.     The  quality  of  any  material  as 
a  conductor   is   expressed   by   the   letter    (K),   which   has   a 
definite  value  for  every  substance. 

33.  Meaning  of  K. — The  physical  meaning  of  (K)  in  equa- 
tion   (32)    may   be   readily   determined   by   making    (Z)    and 
(A)  equal  to  unity.    Then  length  (I)  may  be  measured  in  any 
unit  of  length  and  the  area    (A)    may  be  measured   in  any 
unit  of  area.      (K),  then,  is  the  resistance  of  a   conductor 
of  unit  length  and  unit  cross-section,  and  there  will  be  as 
many  values  of   (K)    as  there  are  units  in   which   we  may 
measure    (?)  and  (A).    There  are  two  values  of  (K)  that  are 
in  common  use  and  these  only  will  be  considered.     They  are 
the  specific  resistance  and  the  mil-foot  resistance. 

34.  Specific   Resistance. — If  the  length  of  a   conductor   is 
one  centimeter  and  its  cross-section  one  square  centimeter, 
then,  by  equation   (32),  we  have  R  =  K;   that  is,   (K)   is  the 
resistance  of  a  cubic  centimeter  of  the  material  considered. 
If  the  length  of  the  conductor  is  one  inch  and  the  area  one 
square  inch,  then  (K)   is  equal  to  the  resistance  of  a  cubic 
inch  of  the  material.     The  resistance  of  a  cubic  centimeter 
or  cubic  inch  of  any  material  is   called  the  specific   resist- 
ance of  the  material,  and  it  is  usually  expressed  in  microhms 
at  0°  centigrade.     (A  microhm  is  the  one-millionth  part  of 
one  ohm. 

35.  Circular  Mil. — In  the  majority  of  cases  electrical  con- 
ductors have  a  circular  cross-section  and  when  we  calculate 
the  cross-sectional  area  from  the  diameter,  the  awkward  fac- 
tor .7854,  or  (7r-^-4),  appears.    To  avoid  this  factor  a  more  con- 
venient practical  unit  of  area  has  been  adopted — the  circular 
mil    (c.m.).     The  circular  mil  is  the  area  of  a  circle  whose 


CALCULATION  OF  EESISTANCE  39 

diameter  is  one  mil  or  .001  of  an  inch.  The  square  mil, 
on  the  other  hand,  is  the  area  of  a  square  whose  side  is  one 
mil.  The  advantage  in  the  use  of  the  circular  mil  is  that 
when  the  diameter  of  the  conductor  is  given  in  mils,  its  cir- 
cular-mil area  may  be  determined  by  squaring  the  diameter. 
Conversely,  the  diameter  may  be  determined,  when  the  cir- 
cular-mil area  is  given,  by  taking  the  square  root  of  the 
area.  This  gives  the  diameter  in  mils  and  from  it  the  diame- 
ter in  inches  may  be  obtained  by  dividing  by  one  thousand. 

36.  Mil-Foot  Resistance. — The  mil-foot  resistance  of  a  ma- 
terial is  defined  as  being  the  resistance  of  a  volume  of  the 
material  one  foot  in  length  and  having  a  uniform  cross-sec- 
tion of  one  circular  mil.  Then  if  (I)  is  equal  to  one  foot 
and  (A)  is  equal  to  one  circular  mil,  in  equation  (32)  (K) 
will  be  equal  to  (R).  The  mil-foot  resistance  is  really  a 
particular  value  for  the  specific  resistance, '  as  it  is  the  re- 
sistance of  a  certain  volume. 

Values  of  Specific  and  Mil-Foot  Resistance. — The  values 
of  the  specific  resistances  of  some  of  the  common  materials 
are  given  in  Table  No.  IV. 


TABLE  NO.  IV 

SPECIFIC. RESISTANCE,  PER  CENT  RELATIVE  RESISTANCE  AND 
CONDUCTANCE,    OF   DIFFERENT   MATERIALS 


Material 

Measurements  at  0°  Centigrade 

Relative 
Resist- 
ance % 

Relative 
Conduc- 
tivity % 

Microhms 
per  cubic 
cm. 

Microhms 
per  cubic 
inch 

Mil- 
foot 
res. 

Copper  (Matthies- 
sen's  Standard) 
Copper,  annealed,. 
Silver  

1.594 
1.56 
1.47 
5.75 
9.07 
20.4 

8.98 
94.3 

2.2 
2.  6 

.6276 
.614 
.579 
2.26 
3.57 
8.04 

3.53 
37.1 

.865 
1.01 

9.54 
9.35 
8.82 
34.5 
54.5 
123. 

53.9 
566. 

13.2 
15.4 

100.0 
97.5 
92.5 
362. 
570. 
1280. 

565. 
5930. 

138. 
161. 

100.0 
102.6 
108.2 
27.6 
17.6 
7.82 

17.17 
1.69 

72.5 
62.1 

Zinc  (pure)  
Iron  (very  pure).. 
Lead  (pure)  
Platinum     (  a  n  - 
nealed) 

Mercury     

Gold    (practically 
pure) 

A.1  u  m  i  n  u  m  (99% 
pure)  

30  PKACTICAL  APPLIED  ELECTK1CITY 

The  above  values  are  based  upon  Matthiessen's  determina- 
tion of  what  he  thought  to  be  the  specific  resistance  of  pure 
copper.  The  copper  he  used,  however,  contained  considerable 
impurities  and  as  a  result  the  copper  obtainable  at  the  pres- 
ent time  has  a  specific  resistance  less  than  that  determined 
by  Matthiessen  in  1860. 

37.  Relative  Conductivity. — The  conductivity  of  a  mate- 
rial is  equal  to  the  reciprocal  of  its  specific  resistance.  The 
relative  conductivity  of  any  material  would  be  the  percent- 
age relation  between  the  conductivity  of  the  material  and 
the  conductivity  of  copper,  which  is  taken  as  the  standard: 

Conductivity  of  material 

%  relative  conductivity  =  —  —  x  100,  or 

Conductivity  of  copper 

Specific  resistance  of  copper 
= X  100  (33) 


Specific  resistance  of  material 

The  value  of  the  per  cent  relative  conductivity  of  a  number 
of  different  materials  is  given  in  Table  No.  IV. 

38.  Relative  Resistance. — The  relative  resistance  of  a  ma- 
terial in  per  cent  is  the  relation  between  its  specific  resist- 
ance and  the  specific  resistance  of  the  standard,  multiplied 
by  100: 

%  relative  Specific  resistance  of  material 

resistance     = X  100     (34) 

Specific  resistance  of  standard 

The  value  of  the  per  cent  relative  resistance  of  a  number 
of  different  materials  is  given  in  Table  No.  IV. 

39.  Relation   between   Square  and   Circular-Mil    Measure. — 
In  the  calculation  of  the  resistance  of  electrical  conductors 
it  is  often  necessary  to  change  from  the  square  to  the  circu- 
lar mil  or  vice  versa.     The  relation  of  the  area  represented 
by   one   circular  mil   as   compared   to   the   area   represented 
by  one  square  mil  can  be  easily  shown  by  reference  to  Fig.  5. 
The   small   square   in   the   figure   represents   an    area   corre- 
sponding to  100  square  mils   (these  areas  are  greatly  exag- 
gerated in  the  figure).     A  circle  drawn  inside  the  square  as 


CALCULATION   OF  KES1STANCE 


31 


shown  will  have  an  actual  area  less  than  the  square.  The 
area  of  the  square  in  square  mils  is  equal  to  the  product 
of  the  two  sides  measured  in  mils,  or  it  is  the  value  of  the 
side  in  mils  squared.  The  circle  has  an  area  in  square  mils 
equal  to  the  diameter  squared  times  .7854,  or  the  area  of 
the  circle  is  .7854  of  the  area  of  the  square.  Now  the  area 
of  the  circle  in  circular  mils  (by  definition  of  the  circular 
mil,  Sec.  35)  is  equal  to  the  diameter  in  mils  squared  (d)2. 

The  number    of    square    mils    en- 

closed  by   the    circle   will   then   be 

equal  to  .7854  of  the  number  of 
circular  mils  enclosed  by  the  circle, 
or  the  actual  area  corresponding  to 
a  circular  mil  is  less  than  the  area 
corresponding  to  one  square  mil. 
This  results  in  there  always  being 
a,  greater  number  of  circular  mils 
in  any  area  than  there  are  square 
mils.  To  change  from  circular  to 
square  mils,  multiply  the  area  in 
circular  mils  by  .7854  and  the  result 
is  the  area  in  square  mils.  Or,  to 

change  from  square  to  circular  mils,  divide  the  area  in  square 
mils  by  .7854  and  the  quotient  thus  obtained  will  be  the  area 
in  circular  mils. 

Example. — The  diameter  of  a  circular  copper  conductor 
is  102.0  mils.  Determine  the  area  of  the  above  conductor  in 
both  circular  and  square  mils. 

Solution.— The  area  of  any  circular  conductor  in  circular 
mils  is  equal  to  the  diameter  of  the  conductor  in  mils, 
squared,  or 

Circular-mil  area  =  d2  =  (102.0)2  =  10  404 

Ans.     10  404  circular  mils. 

(2)  The  area  of  a  circle  in  square  measure  is  equal  to 
.7854  times  the  diameter  of  the  circular  squared,  or 

Square  mil  area  =  .7854  X  d-  =  .7854  X  (102.0)2  =  8171.3 

Ans.     8171.3  square  mils. 

40.  Calculation  of  Resistance  from  Dimensions  and  Spe- 
cific Resistance. — The  resistance  of  any  conductor  may  be 


Fig.  5 


32  PRACTICAL  APPLIED  ELECTRICITY 

calculated  by  the  use  of  equation  (32)  if  the  dimensions  of 
the  conductor  and  the  value  of  (K)  are  known.  The  value 
of  the  constant  (K)  used  in  the  equation  will,  of  course, 
depend  upon  the  units  used  in  expressing  the  length  and 
area  of  the  conductor.  When  the  length  (Z)  of  the  conductor 
is  expressed  in  feet  and  the  area  (A)  in  circular  mils,  the 
constant  (K)  corresponds  to  the  mil-foot  resistance  of  the 
material.  The  value  of  this  constant  for  different  materials 
can  be  obtained  from  Table  No.  II.  The  mil-foot  resistance  of 
commercial  copper  at  25°  centigrade  is  approximately  10.8. 

41.  Wire   Gauges. — For  many  purposes   it  is   desirable   to 
designate  the  size  of  a  wire  by  gauge  numbers  rather  than 
by   a   statement  of   their   cross-section.     A   number   of   wire 
gauges  have  been  originated  by   different  manufacturers  of 
wire,  such  as  the  B.  &  S.  gauge,  commonly  called  the  Amer- 
ican   gauge,    Brown    and    Sharpe    Manufacturing    Company, 
which  is  the  one  generally  used  in  this  country.     In  the  meas- 
urement of  iron  and  steel  wire  the  "Birmingham  wire  gauge" 
(B.  W.  G.),  or  Stub  gauge  is  usually  used.    There  are  a  num- 
ber   of    other    gauges    such    as    the    Roebling,    Edison,    and 
New  British   standard,   but  these  are  not  used  very   much. 
The  diameters  in  mils  of  the  different  size  wires  is  given 
in  Table  D,  Chapter  20. 

The  B.  &  S.  gauge  is  by  far  the  most  common  wire  gauge 
in  use  in  this  country  and  for  that  reason  it  will  be  used 
almost  entirely  in  wiring  calculations.  Tables  E  and  F, 
Chapter  20,  give  the  properties  of  copper  wire. 

42.  How  to    Remember  the   Wire   Table. — The  wire  table 
has  a  few  simple  relations,  such  that  if  a  few  constants  are 
carried  in  the  memory,  the  whole  table  can  be  constructed 
mentally   with   approximate    accuracy.     The    chief   relations, 
without  proof,  may  be  enumerated  below  and  verified  from 
the  table. 

The  following  approximate  relations  should  be  remembered: 
No.  10  B.  &  S.  gauge  wire  is  100  mils  in  diameter,  approxi- 
mately; has  an  area  of  10000  c.m.;  has  a  resistance  of  one 
ohm  per  thousand  feet;  and  weighs  31.43  pounds  per  thou- 
sand feet,  at  20°C.  (68°F.).  No.  5  wire  weighs  100.2  pounds 
per  1000  feet.  The  following  rules  are  approximately  true 
for  B.  &  S.  gauge  wire. 


CALCULATION  OF  RESISTANCE  33 

(a)  A  wire  which  is  three  sizes  larger  than  another  has 
half  the  resistance,  twice  the  weight,  and  twice  the  area. 

(b)  A  wire  which  is  ten  sizes  larger  than  another  has  one- 
tenth   the   resistance,   ten  times   the   weight,   and   ten   times 
the  area. 

(c)  To    find  the  resistance,  divide  the  circular-mil  area  by 
10;  the  result  is  the  number  of  feet  per  ohm. 

(d)  To    find    the    weight    per    thousand    feet,    divide    the 
number  of  circular  mils  by  10  000  and  multiply  by  the  weight 
of  No.   10  wire.     Table  C,  Chapter  20,  gives  the  equivalent 
cross-sections  of  different  size  wires. 

PROBLEMS 

(1)  What  is  the   circular-mil   area  of  a  wire   *4   inch   in 
diameter? 

Ans.     62  500  c.m. 

(2)  The  circular-mil  area  of  a  wire  is  4225.     What  is  its 
diameter  in  inches? 

Ans.     .065  inch. 

(3)  A  certain  rectangular  piece  of  copper  is  %  by  Vz  of 
an  inch   in   cross-section.     What  is  the   area  of  this   bar  in 
square  mils? 

Ans.     125000  sq.  mils. 

(4)  What  is  the  area  of  the  rectangular  piece  of  copper 
given   in   problem   3,   in   circular   mils? 

Ans.     Approximately,  159  150  c.m. 

(5)  What    would    be    the    diameter    of    a    circular    con- 
ductor in  mils  that  would  have  the  same  actual  area  as  the 
rectangular  piece  of  copper  given  in  problem  3? 

Ans.    Approximately  399.  mils. 


CHAPTEK  III 


SERIES    AND    DIVIDED    CIRCUITS— MEASUREMENT     OF 
RESISTANCE 

43.  Grouping  of  Conductors. — The  resistance  of  a  whole  or 
a  portion  of  a  circuit  will  depend  upon  the  manner  in  which 
the  various  parts  constituting  the  circuit  are  connected. 
Two  or  more  conductors  may  be  combined  in  a  number  of 
ways,  and  the  total  resistance  of  the  combination  can  be 
determined  if  the  resistance  of  each  part  of  the  circuit  and 
the  manner  in  which  the  various  parts  are  connected  is 
known.  The  various  ways  in  which  conductors  may  be 
grouped  are  as  follows: 

(a)  Series  grouping. 

(b)  Parallel  or  multiple  grouping. 

(c)  Any  combination  of  series  and  parallel. 

44.  Series  Grouping. — 
When  the  conductors  form- 
ing a  circuit  are  so  ar- 
ranged that  the  current  has 
a  single  path  the  conductors 
are  said  to  be  connected 
in  series  and  such  a  circuit 
is  called  a  series  circuit. 
Fig.  6  shows  three  resist- 
ances (Ri),  (R2),and  (R8), 
connected  in  series  to  the 
Fig-  6  terminals  of  the  battery 

(B).    The  current  has  only 

one  path  from  the  positive  to  the  negative  terminal  of  the 
battery.  These  resistances  may  be  of  widely  different  values 
and  composed  of  different  materials,  but  the  total  resistance 
of  the  combination  is  equal  to  the  sum  of  the  resistances  of 
the  various  parts. 

Suppose  the  three  resistances  in  Fig.  6  have  values  of  3, 
4,  and  5  ohms,  then  the  total  resistance  of  the  circuit,  neg- 

34 


~Jn  r 

,TTh  i 

B 

B 

SERIES  AND  DIVIDED  CIRCUITS 


35 


lecting  the   resistance   of   the   connections   and   the   internal 
resistance  of  the  battery,  will  be  3  +  4  +  5  =  12  ohms. 

The  above  relation  of  the  total  resistance  to  the  individual 
resistances  can  be  shown  by  a  hydraulic  analogy.  Suppose 
that  in  Fig.  7  (A),  (B),  and  (C)  are  three  pipes  of  different 
size  and  length  and  that  they  are  joined  end  to  end,  or  in 


Fig.  7 


series,  and  they  are  to  be  used  in  conducting  water  from 
the  tank  (Tj)  to  the  tank  (T2).  It  is  apparent  that  the  total 
resistance  offered  by  the  three  pipes  connected  in  series  is 
equal  to  the  sum  of  their  respective  resistances. 

45.  Facts  Concerning  Series  Circuit. — There  are  four  facts 
concerning  every  series  circuit: 

(a)  The  current  is  uniform  throughout  the  series  circuit. 

(b)  The  p.d.'s  over  any  portions  of  the  series  circuit  are 
proportional  to  the  resistances  of  these  portions. 

(c)  The    total    resistance    is   the    sum    of   the    individual 
resistances. 

(d)  The   effective   e.m.f.   of   the    circuit   is   the   algebraic 
sum  of  all  the  e.m.f.'s  acting  in  the  circuit. 

46.  Uniformity   of  Current. — Since  there   is   but  one  path 
for  the   current,  the   conductors   being  all  joined   in   series, 
there  must  be  as  much  current  at  one  end  of  the  conductor 
as  at  the  other.     If  this  were  not  the  case  there  would  be 
an  accumulation  of  electricity  at  certain  points  along  the  cir- 
cuit,  but   careful    experiments    show   no    such    accumulation. 
The  flow  of  electricity  can  be  compared  to  the  flow  of  water 
or  other  incompressible  fluid  in  a  pipe,  as  shown  in  Fig.  7. 
If   there    is    a    certain    quantity   of    liquid    entering    the    end 
of  the  pipe,  connected  to  the  tank   (Tj),  in  a  certain  time, 


36  PRACTICAL  APPLIED  ELECTRICITY 

then  that  same  quantity  must  pass  by  any  cross-section  of 
the  pipe  and  the  same  quantity  must  flow  out  of  the  other 
end  of  the  pipe  in  the  same  time.  It  is  impossible  for  the 
liquid  to  accumulate  at  any  point  as  it  is  incompressible. 

An  ammeter,  which  is  an  instrument  used  to  measure  the 
current,  may  then  be  connected  at  any  point  in  a  series  cir- 
cuit and  there  will  be  the  same  indication  on  its  scale  so  long 
as  the  total  resistance  of  the  circuit  and  the  electrical  pres- 
sure acting  on  the  circuit  remain  constant.  It  must  always 
be  remembered  that  it  is  not  the  current  in  an  electrical 
circuit  that  is  used  up,  but  instead,  it  is  the  energy  of  the 
electricity  that  is  always  utilized. 

47.  Relation  of  P.D.'s  to  Resistance. — Ohm's  Law,  which 
expresses  the  relation  between  electrical  pressure,  current, 
and  resistance,  holds  for  any  part  of  the  circuit  as  well 
as  for  the  whole  circuit.  Consider  a  uniform  conductor 


Fig.  8 

(A,  B,  C,  D),  carrying  a  current  of  (I)  amperes  in  the  direction 
indicated  by  the  arrow  in  Fig.  8.  There  must  be  a  difference 
in  pressure  between  the  points,  say  (A)  and  (B),  since  there 
is  a  current  between  them  and  the  point  (A)  is  at  a  higher 
potential  or  pressure  than  the  point  B  when  the  current 
exists  in  the  direction  indicated.  Let  the  resistance  between 
the  points  (A)  and  (B)  be  represented  by  (Ri)  and  the 
difference  in  pressure  or  drop  in  potential  between  the  same 
two  points  be  represented  by  (Ej).  The  current  is  then  equal 
to  (Ei)  divided  by  (Ri),  or 

E! 
I  =  —  (35) 

RI 

If  any  other  section  of  the  conductor  be  taken,  such  as 
that  between  the  points  (C)  and  (D),  and  the  drop  in  poten- 
tial between  the  two  points  be  represented  by  (E2)  and 
the  resistance  of  the  section  by  (R2)  we  have 

E2 
I  =  -  (36) 

R2 


SEEIES  AND  DIVIDED  CIRCUITS  37 

The  currents  in  the  two  sections  are  equal  since  they  are 
in  series  and  the  right-hand  portions  of  the  above  equations 
are  equal,  hence 

B!      E2 

(37) 
RI      R2 

or  the  drop  in  potential  is  proportional  to  the  resistance. 

Example.  —  Two  coils  of  5  and  10  ohms  are  connected  in 
series  to  a  battery  whose  e.m.f.  is  6  volts.  What  is  the  poten- 
tial drop  over  each  coil? 

Solution.  —  From  equation  (37)  we  can  determine  the  rela- 
tion between  (Ej)  and  (E2),  where  they  represent  the  drops 
in  potential  over  the  two  coils,  by  substituting  the  values 
of  (Ri)  and  (R2)  in  the  equation,  which  gives 


5       10 
5  E2  =  10  E! 

EO     TTS 
2  ===     ^    -*^1 

The  p.d.  (E2)  over  the  10-ohm  coil  is  then  equal  to  twice 
the  p.d.  (EO  over  the  5-ohm  coil.  The  5-ohm  coil  will  then 
have  %  of  the  total  pressure  over  it  and  the  10-ohm  coil  will 
have  %.  Since  the  total  pressure  is  6  volts,  the  drop  over  the 
5-ohm  coil  will  be 

i/,  of  6  =  2 

Ans.     2  volts. 
and  the  p.d.  over  the  10-ohm  coil  will  be 

%  of  6  =  4 

Ans.     4  volts. 

48.  Resistance  of  Series  Circuit.—  In  a  previous  section 
the  statement  was  made  that  the  total  resistance  of  the  series 
circuit  is  equal  to  the  sum  of  the  various  resistances  com- 
posing the  circuit.  This  statement  is  practically  self-evident, 
but  it  may  be  shown  to  be  true  by  an  application  of  Ohm's 
Law. 

If  a  number  of  resistances  (Rj),  (R2),  etc.,  are  connected 
in  series  and  there  is  a  current  of  (I)  amperes  through  them, 
we  have,  from  equation  (35), 


38  PRACTICAL  APPLIED  ELECTRICITY 

E1  =  R1I,  E2  =  R2I,  etc.,        (38) 

where    (Ej),    (E2),  etc.,  represent  the  p.d.'s  over  the  resist- 
ances (Ri),  (R2),  etc. 

Let  (R)  represent  the  total  resistance  and  (E)  the  total 
pressure.  Then 

E  =  RI  (39) 

But  we  also  know  (E)  is  equal  to  the  sum  of  all  the  p.d.'s, 
that  is, 

Hence 

RI  =  R,I  +  R2I  +  etc.  (41) 

R  =  Rt  +  R2  -f  etc.  (42) 

The  above  equation  states  that  the  resistance  of  several 
conductors  joined  in  series  is  the  sum  of  their  individual 
resistances. 

Example. — Three  resistance  coils  of  5,  6,  and  7  ohms,  re- 
spectively, are  connected  in  series  and  the  combination  con- 
nected to  a  battery  whose  e.m.f.  is  9  volts.  What  is  the 
value  of  the  current  in  the  coils? 

Solution. — The  total  resistance  (R)  is  equal  to  the  sum 
of  the  several  resistances,  or 

R  =  5  +  6  +  7  =  18  ohms 

The  current  then  is  equal  to  (E)  divided  by  (R),  or 

9        1 

18        2 

Ans.     l/2  ampere. 

If  there  are  (n)  equal  resistances  of  (r)  ohm  each  con- 
nected in  series,  the  total  resistance  (R)  is 

R  =  nr  (43) 

An  example  of  this  would  be  a  number  of  lamps  connected 
in  series  and  the  combination  then  connected  to  the  mains. 
If  there  are  5  incandescent  lamps  connected  in  series  each 
having  a  resistance  of  220  ohms,  the  combination  will  have  a 
resistance  of  5  X  220,  or  1100  ohms. 

49.  Effective  E.M.F.  in  a  Circuit. — The  effective  e.m.f.  in 
a  circuit  is  the  e.m.f.  that  is  really  effective  in  causing  the 
current.  Several  sources  of  e.m.f.  may  be  joined  in  series, 


SERIES  AND  DIVIDED  CIRCUITS 


39 


but  the  effective  e.m.f.  would  not  necessarily  be  equal  to  the 
sum  of  their  values  because  some  of  the  e.m.f.'s  might  act 
in  the  opposite  direction  to  others.  If  all  the  e.m.f.'s  in 
the  circuit  tend  to  send  a  current  in  the  same  direction  then 
the  value  of  the  effective  e.m.f.  is  the  sum  of  all  the  e.m.f.'s 
acting.  When  they  are  not  all  acting  in  the  same  direction, 
the  effective  e.m.f.  is  equal  to  the  difference  between  the 
sum  of  the  e.m.f.'s  acting  in  one  direction  and  the  sum  of  the 
e.m.f.'s  acting  in  the  opposite  direction,  and  its  direction  will 
be  that  of  the  larger  sum.  An  example  of  the  above  would 
be  a  battery  composed  of  a  number  of  cells  all  connected  in 
series  but  the  e.m.f.  of  some  of  the  cells  acting  in  the  oppo- 
site direction  to  the  remainder.  The  effective  e.m.f.  is  a 
maximum  when  all  the  e.m.f.'s  in  the  circuit  are  acting  in 
the  same  direction. 

50.  Parallel  or  Multiple  Grouping. — When  the  conductors 
forming  a  circuit  are  so  connected  that  there  are  as  many 
paths  for  the  current  as  there  are  conductors,  the  conductors 
are  said  to  be  connected  in  parallel  or  multiple,  and  such  a 

circuit  is  called  a  divided 

circuit.    Fig.  9  shows  three 

coils  (Ri),  (R2),  and  (R3) 
connected  in  parallel  and 
the  combination  connected 
to  the  battery  (B).  In  a 
circuit  such  as  that  shown 
in  Fig.  9,  it  is  apparent 
that  the  current  cannot  be 
the  same  in  all  parts  of  the 
circuit,  since  it  divides  at 
the  point  (A)  between  the 

branches,  part  existing  in  each  branch.  The  part  of  the  total 
current  that  is  in  each  branch  will  depend  upon  the  relation 
between  the  resistance  of  that  particular  branch  to  the  re- 
sistance of  the  other  branches. 

The  total  resistance  is  not  equal  to  the  sum  of  the  several 
resistances,  as  in  the  series  circuit,  but  it  will  be  less  than 
the  resistance  of  the  branch  having  the  smallest  resistance. 
A  simple  hydraulic  analogy,  as  shown  in  Fig.  10,  will  serve 
to  verify  the  above  statements.  Three  pipes,  (Pj),  (P2), 
and  (P3)  are  used  in  conducting  water  from  a  tank  (Tj) 


Fig.   9 


40 


PRACTICAL  APPLIED  ELECTRICITY 


to  another  tank  (T2),  as  shown  in  the  figure.  If  the  pressure 
in  the  tank  (Tj)  is  maintained  constant,  the  pressure  acting 
on  the  three  pipes  will  remain  constant  and  it  will  be  the 
same  for  each  pipe,  neglecting  the  difference  in  their  level. 

The  same  pressure  is  act- 
ing on  each  of  the  resist- 
ances in  Fig.  9,  neglecting 
the  resistance  of  the  con- 
necting leads.  Let  this 
pressure  be  represented  by 
(E).  The  current  in  each 
of  the  resistances  will  be 
Fig.  10  •  equal  to  the  presure  over 

the  branch,  which  in  this 

case  is  (E),  divided  by  the  resistance  of  the  branch.  The 
current  supplied  by  the  battery  is  equal  to  the  sum  of  the 
currents  in  the  various  branches,  just  as  the  total  quantity  of 
water  flowing  from  the  tank  (Ti),  Fig.  10,  in  a  given  time, 
is  equal  to  the  sum  of  the  quantities  flowing  in  the  three 
pipes  in  the  same  time.  Representing  the  currents  in  the 
several  branches  by  (Ii),  (I2),  and  (I3),  and  the  total  current 
by  (I)  we  have  the  relation 


I  =  I,  +  I2  + 


E 

Ii  =  — 
B, 


E 


(44) 
(45) 


R3 


The  total  current  (I)  is  equal  to  the  electrical  pressure 
(E)  acting  on  the  combination  divided  by  the  total  resist- 
ance (R)  which  we  want  to  determine,  or 


(46) 


Substituting  the  values  of  the  various  currents  in  equation 
(44),  we  have 


E        E        E       E 

—  =  -  +  --  +  - 
R       RI      R2      RS 


(47) 


SERIES  AND  DIVIDED  CIRCUITS  41 

Dividing  both  sides  of  the  equation  by  (E),  we  have 

1111 

-  =  —  +  --  +  -  (48) 

R       R,       Ro       R3 

The  above  equation  states  that  the  total  conductance  of  a 
number  of  resistances  in  parallel  is  equal  to  the  sum  of  the 
respective  conductances  regardless  of  the  number  connected. 
This  equation  can  be  reduced  to  the  form 

RjR2R3 

R  =  — (49) 

RiR2  ~h  -^2^3  H~  RiRs 

When  there  are  only  two  resistances  connected  in  parallel, 
the  combined  resistance  can  be  calculated  by  the  use  of  the 
equation 

RjR2 

R  = (50) 

RI  +  R2 

If  the  resistances  (Ri)  and  (R2)  are  equal,  the  combined 
resistance  is  equal  to  one-half  of  the  resistance  of  either 
of  them.  Or,  in  general,  if  (n)  equal  resistances  of  (r)  ohms 
each  are  connected  in  parallel,  the  combined  resistance  (R)  is 

r 
R  =  —  (51) 

n 

Example. — Eight  incandescent  lamps,  each  having  a  resist- 
ance of  220  ohms,  are  connected  in  parallel  across  a  110-volt 
circuit.  What  is  the  total  current  taken  by  the  lamps? 

Solution. — The  total  resistance  of  the  eight  lamps  would  be 
equal  to  the  resistance  of  one  of  them  divided  by  the  number 
of  lamps  connected  in  parallel,  or 
r        220 

R  =  —  = =  27^  ohms 

n         8 

The  current  taken  by  the  lamps  is   equal  to  the  applied 
voltage  divided  by  the  resistance,  or 
E        110 

I  =  —  = =  4 

R      27V2 

Ans.    4  amperes. 


42  PEAGTICAL  APPLIED  ELECTRICITY 

Example. — Two  resistances  of  3  and  5  ohms,  respectively, 
are  connected  in  parallel.  What  is  their  combined  resist- 
ance? 

Solution. — The  combined  resistance  can  be  determined  by 
substituting  directly  in  equation  (50),  which  gives 

3X5       15 

R  =  =  1% 

3  +  5        8 

Ans.     1%   ohms. 

51.     Series   and    Parallel    Combinations. — A    number   of  re- 
sistances may  be  connected  in  such  a  way  that  some  of  them 
are  in  parallel  with  others,  or  some  of  them  may  be  in  series 
with  others,  or  a  combination  of  series  and  parallel  connec- 
tions may  be  formed.     Six  resistance  coils  are  shown  con- 
nected together  in  Fig.  11. 
This  is  a  parallel  combina- 
R^.  R5  tion  of  three  different  re- 

I J\fflfo        '^N^f^\  sistances,      the      first      of 

R2      4     R,\  which   consists   of  the   re- 

sistances     (R4)    and    (Rr)) 
2X2       Re  2  3f/2  /  in  series;   the  second  con- 

•tyWWWV '  sists  of  (Ri)'  ^^'  and 

6  (R3)    in    series;     and    the 

third  consists  of  the  single 

Fl2      11 

resistance    (R6).     To   find 
the  total  resistance  of  the 

circuit  determine  the  resistance  of  each  path  separately  and 
combine  their  resistances  by  the  use  of  equation  (49). 

Several  such  groups  of  resistances  may  be  connected  in 
series  and  the  total  resistance  would  be  the  sum  of  the 
resistances  of  the  several  groups. 

Example. — The  six  coils  shown  connected  in  Fig.  11  have 
the  resistances  marked  on  them  in  the  figure.  What  is  the 
total  resistance? 

Solution. — The  resistance  of  the  upper  branch,  call  it  (Bj), 
is  equal  to  th^  sum  of  the  resistances  (R4)  and  (R5),  these 
being  connected  in  series,  or 

Bi  =  3  +  4  =  7  ohms 

Similarly  the  resistance  of  the  middle  branch   (B2)  is 
B2  ==  2y2  +  2  +  3V»  =  8  ohms 


SERIES  AND  DIVIDED  CIRCUITS  43 

and  the  resistance  of  the  lower  branch  (B3)  is  6  ohms.  Sub- 
stituting these  values  for  the  resistances  of  the  various 
branches  in  equation  (49),  we  obtain 

7X8X6  336 

R  = = =  2.301 

7X8  +  7X6  +  8X6       146 

Ans.     2.301  ohms. 

PROBLEMS  ON  SERIES  AND  DIVIDED  CIRCUITS 

(1)  Five    similar    incandescent    lamps    are    connected    in 
series   across   550-volt  mains,   and   there   is   a   current  of   .5 
ampere  through  them.     What  is  the  combined  resistance  of 
the  five  lamps  and  the  resistance  of  each? 

Ans.     Combined  resistance,  1100  ohms. 
Resistance  of  each  lamp,  220  ohms. 

(2)  An  adjustable  resistance  is  connected  in  series  with 
the  field  winding  of  a  dynamo,  which  has  a  resistance  of  40 
ohms,  and  a  current  of  2  amperes  exists  in  the  circuit  when 
the  impressed  voltage  is  110  volts.     What  is  the  total  resist- 
ance of  the  circuit,  and  how  many  ohms  resistance  is  there 
in  the  circuit  due  to  the  adjustable  resistance? 

Ans.     Total  resistance,  55  ohms. 

Adjustable  resistance,  15  ohms. 

(3)  There  is  a  current  of  50  amperes  in  a  circuit  when  the 
impressed  voltage  is  200  volts.     What  resistance  should  be 
added  in  series  with  the  circuit  in  order  that  the  current  be 
reduced  to  40  amperes? 

Ans.     1  ohm. 

(4)  What  resistance  should  be  connected  in  parallel  with 
the  circuit  in  problem  3  when  the  current  is  50  amperes  in 
order  that  the  total  current  may  be  80  amperes? 

Ans.     6%  ohms. 

(5)  Three  resistances  of  5,  6,  and  7  ohms,  respectively,  are 
connected  in  parallel.     What  is  their  combined  resistance? 

Ans.     1.96  ohms. 

(6)  If  12  similar  incandescent  lamps  connected  in  parellel 
have  a  combined  resistance  of  18%  ohms,  what  is  the  resist- 
ance of  each  lamp? 

Ans.     220  ohms. 


44  PRACTICAL  APPLIED  ELECTRICITY 

(7)  Two  resistances  of  4  and  12  ohms,  respectively,  are 
connected  in  parallel  and  the  combination  connected  in  series 
with  a  7-ohm  coil.    What  is  the  current  through  each  resist- 
ance  when   a   pressure   of  50   volts   is   impressed   upon   the 
circuit? 

Ans.  Current  in  7-ohm  coil,  5  amperes. 
Current  in  12-ohm  coil,  1^4  amperes. 
Current  in  4-ohm  coil,  3%  amperes. 

(8)  What  is  the  drop  in  potential  over  each  resistance  in 
the  above  problem?    What  resistance  should  be  introduced  in 
the  circuit,  and  how,  to  make  the  value  of  the  current  2.5 
amperes? 

Ans.  Drop  over  7-ohm  coil,  35  volts. 
Drop  over  4-ohm  coil,  15  volts. 
Drop  over  12-ohm  coil,  15  volts. 
Connect  10  ohms  in  series. 

52.  Measurement  of  Resistance. — Practically  all  the  meth- 
ods employed  in  measuring  resistance  depend  upon  some  ap- 
plication of  Ohm's  law.    The  method  to  be  used  in  any  case 
will   depend   upon    the   kind   of  resistance   to   be   measured, 
that  is,  whether  it  is  capable  of  carrying  a  large  or  small  cur- 
rent;   the  accessibility  of  the   resistance;    the  value   of  the 
resistance  to  be  measured;   and  the  accuracy  desired.     The 
different  methods  described  in  the  following  sections  are,  per- 
haps, the  most  common  ones  employed  in  practice. 

53.  Drop   in    Potential    Method. — Since   Ohm's   Law   holds 
true   for   any  part   of  an   electrical   circuit,   it   follows   that 
the  value  of  a  certain  resistance  can  be  determined  by  measur- 
ing the  drop  in  potential  across  the  resistance  when  the  cur- 
rent through  the  resistance  is  known.     A  voltmeter  for  meas- 
uring   the    drop    in    potential,    an    ammeter    for    measuring 
the  current,  and  some  source  of  energy  such  as  a  battery  or 
generator  are  required  in  measuring  resistance  by  this  method. 
The  resistance  (R)  to  be  measured  is  connected  in  series  with 
the  ammeter    (A),   and  the   combination  then   connected   to 
the  source  of  energy  such  as  a  battery  (B),  indicated  in  Pig. 
12.    The  drop  in  potential  across  the  resistance  can  be  deter- 
mined  by   means    of   the    voltmeter    (V),   which    should   be 
connected  to  the  terminals  of  the  resistance,  as  shown  in  the 
figure.     The  value  of  the  resistance  can  be  determined   by 


SEEIES  AND  DIVIDED  CIRCUITS 


45 


substituting  the  ammeter  and  voltmeter  readings  in  equation 
(5),  which  states  that  the  resistance  is  equal  to  the  differ- 
ence in  electrical  pressure  divided  by  the  current.  This  is  a 
very  simple  and  convenient  method  and  will  give  quite  accur- 


Fig.  12 

ate  results  when  proper  care  is  exercised  in  reading  the  in- 
struments. The  method  is  best  suited  for  the  measurement  of 
low  resistances  capable  of  carrying  rather  large  currents,  for 
the  following  reason :  The  current  in  the  resistance  to  be  meas- 
ured is  not  equal  to  that  indicated  on  the  ammeter  because 
there  is  a  certain  current  through  the  voltmeter.  The  current 
through  the  voltmeter  will,  however,  be  small  in  comparison 
to  that  through  the  unknown  resistance,  if  the  resistance  of 
the  voltmeter  is  large  in  comparison  to  the  unknown,  the  cur- 
rents in  the  two  branches  of  a  divided  circuit  being  to  each 
other  inversely  as  the  resistances  of  the  respective  branches. 
This  error  can  be  avoided  by  subtracting  from  the  value  of 
the  current  indicated  on  the  ammeter  the  value  of  the  cur- 
rent through  the  voltmeter,  which  gives  the  true  value  of  the 
current  through  the  resistance  to  be  measured.  The  current 
through  the  voltmeter  is  equal  to  its  indication  in  volts 
divided  by  its  own  resistance,  or 

E 
I,  =  —  (52) 

Ry 

The   resistance   of  the   voltmeter  is  usually  given  on  the 
lid  of  the  containing  case.     If  not,  it  can  be  determined  by 


4<;  I'K.M    11.   Al.    Al'l'l.ll.l.    l-.l,l..  TBI<    II  V 

means  of  a  resistan- .    bridge.     The  current    ir   thrmiKh  the 
resistance  then  in 

Ir«K  — U  or 

E 

It -I.-  (54) 

R* 

and  tho  value  of  the  unknown  resistance  will  \»- 

(55) 


Care  should  be  exercised  in  making  a  resistance  measure- 
tu.  nt  by  thin  method  not  to  pass  too  large  a  current  through 
ilu  object  to  be  measured  as  you  are  likely  to  change  its 
resistance  due  to  a  change  in  temperature  resulting  from 
xcessive  current.  The  greater  the  current,  however, 
without  undue  heating  of  the  conductor,  the  greater  the  volt- 
iii.-t.-r  reading  and,  as  a  UHual  thiiiK.  the  greater  the  accui.-icy. 
When  very  low  resistances  are  to  be  measured,  a  low-read  im; 
\oihn--t.T  or,  better  still,  a  railllvoltmeter  should  be  u 

Example. — The  current  through  a  rail  joint  is  300  amp* •!••  -s 
and  the  drop  in  potential  across  the  joint  and  bonds  is  18 
millivolts  or  .018  volt.  What  is  the  resistance  in  ohms  and 
microhms? 

Solution. — By  substituting  in  equation  (5)  we  have 

.018 

U  «  .000  06 

300 

Ans.    .00006  ohm. 

0.000  06  X  1  000  000  «  60 

Ans.    60  microhms. 

Example. — The  current  through  a  spool  of  wire  is  .5  am- 
pere and  the  drop  in  potential  across  the  spool  as  indi- 
cated on  a  (0-15)  voltmeter,  having  a  resistance  of  1500  ohms, 
is  12  volts.  What  is  the  resistance  of  the  wire? 

Solution. — Substituting  in  equation  (55)  we  have 


SERIES  AND  DIVIDED  CIRCUITS 


12 


R 


X  1500  =  24.39 


.5  X  1500  —  12 

Ans.     24.39  ohms 

54  Measurement  of  Resistance  by  Comparison. — This 
method  requires  no  ammeter  and  the  value  of  the  unknown 
resistance  (X)  is  determined  in  terms  of  a  known  resistance 


Fig.  13 

(R)  connected  in  series  with  it,  as  shown  in  Fig.  13.  The 
drop  in  potential  over  the  known  and  unknown  resistances  is 
measured  when  they  are  both  carrying  the  same  current. 
The  proper  connections  of  the  voltmeter  for  making  these 
measurements  is  shown  in  the  figure  by  the  full  and  dotted 
lines.  Since  the  drop  in  potential  across  any  part  of  a  cir- 
cuit bears  the  same  relation  to  the  drop  across  any  other  part 
of  the  same  circuit  as  exists  between  the  resistances  of  the 
two  parts,  we  have  the  simple  relation 

Drop  in  potential  over  X           Resistance  of  X 
=    (56) 


Drop  in  potential  over  R 


Resistance  of  R 


or 


the  unknown  Resistance  of  R  X  p.  d.  over  X 
resistance  X  = 


(57) 


p.  d.  over  R 

Example. — A  known  resistance  (R)  of  10  ohms  was  con- 
nected in  series  with  an  unknown  resistance  (X),  as  shown  in 
Fig.  13.  The  drop  in  potential  over  (R)  was  5  volts  and  the 
drop  over  X  was  10  volts.  What  was  the  resistance  of  (X)? 


PEACTICAL  APPLIED  ELECTRICITY 


Solution. — Since  the  drop  over  the  resistance  (X)  was  twice 
that  over  the  standard,  the  resistance  of  (X)  must  be  twice 
that  of  the  standard,  or 

X  =  2  X  10  =  20 

Ans.     20  ohms. 

Substituting  in   equation    (57)    we  have 


10  X  10 
X  = =  20 


Ans.     20  ohms. 


55.  Series  Voltmeter  Method.— The  connections  for  the 
measurement  of  resistance  by  this  method  are  made  as 
shown  in  Fig.  14.  The  terminals  (Ta)  and  (T2)  represent 

a  source  of  e.m.f.;   (X)  is 

_  _  the  resistance  to  be  meas- 

I1  o2  ured  and  (V)   is  a  direct 

^J     \ ^          reading  voltmeter.   When 

the  voltmeter  is  con- 
nected as  shown  by  the 
dotted  line,  the  resistance 
(X)  is  not  in  series  with 
it  between  the  terminals 
(Tj)  and  (T2)  and  the 
Fi  14  voltmeter  indicates  the 

total     pressure     between 

the  two  terminals.  When,  however,  the  resistance  (X)  is  con- 
nected in  series  with  the  voltmeter  by  opening  the  switch 
(S),  the  indication  of  the  voltmeter  is  no  longer  the  total 
pressure  between  the  terminals  (Tx)  and  (T2)  but  it  sim- 
ply indicates  the  difference  in  pressure  between  its  own 
terminals.  The  drop  in  potential  over  the  voltmeter  (Ev) 
or  its  own  indication  subtracted  from  the  total  pressure  be- 
tween (Tj)  and  (T2),  which  we  will  call  (E),  will  give  the 
value  of  the  drop  (Ex)  over  the  resistance  (X). 

Ex  =  E  —  Ev  (58) 

It  is  assumed,  of  course,  that  the  difference  in  pressure 
between  (Ta)  and  (T2)  remains  constant.  If  this  is  not  the 
case  a  second  voltmeter  should  be  used,  it  being  connected 
across  the  source  of  supply,  and  the  value  of  its  indication 


SERIES  AND  DIVIDED  CIRCUITS  49 

should  be  noted  at  the  same  time  the  voltmeter  in  series  with 
the  resistance  is  read.  The  current  through  the  voltmeter 
and  the  resistance  (X)  is  the  same,  since  they  are  in  series. 
The  current  through  the  voltmeter  at  any  time  is  equal  to  the 
voltmeter  reading  divided  by  its  own  resistance,  or 

Ev 
Iv=  (59) 

Rv 

The  value  of  the  resistance  (X)  can  now  be  calculated, 
since  the  current  through  it  and  the  drop  in  potential  across 
it  are  known.  Substituting  in  equation  (5)  the  values  of  the 
p.d.  and  the  current  given  in  equations  (58)  and  (59),  gives 

E  —  Ev       E  —  Ev 
R  =  -  X  Rv  (60) 

Ev  Ev 

Rv 

The  above  equation  gives  the  value  of  the  resistance  in 
terms  of  the  total  pressure  (E),  the  voltmeter  reading  (Ev) 
when  it  is  in  series  with  the  resistance,  and  the  resistance 
(Rv)  of  the  voltmeter. 

This  method  is,  in  general,  serviceable  for  the  measure- 
ment of  high  resistances,  such  as  the  insulation  of  electric 
light  and  power  wires  that  are  installed,  insulation  of  trol- 
ley lines,  dynamos,  transformers,  etc. 

The  scheme  of  connections  for  the  measurement  of  the 
resistance  of  the  insulation  of  a  lighting  circuit  is  shown  in 
Fig.  15.  A  small  generator  (G)  capable  of  supplying  an 
e.m.f.  of  about  500  volts  is  usually  used  as  a  source  of  pres- 
sure for  testing.  The  generator  may  be  engine-  or  motor- 
driven.  One  terminal  of  the  generator  is  connected  directly 
to  the  conduit  or  ground  and  the  other  terminal  is  connected 
to  the  wire  whose  insulation  resistance  is  to  be  determined, 
with  the  voltmeter  in  circuit.  The  total  pressure  generated 
by  the  machine  (G)  will  be  distributed  over  the  resistance 
between  the  wire  and  the  conduit,  or  ground,  and  the  volt- 
meter. The  voltmeter  will  read  the  drop  (Ev)  across  itself. 
A  second  voltmeter  (VB)  is  shown  connected  across  the  ter- 
minals of  the  generator,  and  this  voltmeter  will  read  the 
total  pressure  (E).  The  value  of  the  insulation  resistance 


50 


PEACTICAL  APPLIED  ELECTRICITY 


(X)  can  now  be  calculated  by  substituting  the  values  of  The 
readings  of  the  two  voltmeters  in  equation  (60)  together  with 
the  resistance  of  the  voltmeter  (Vx)  and  solving  the  equa- 
tion. Insulation  resistance  is  usually  given  as  so  many 
megohms. 


Exarrple. — Connections  were  made,  as  shown  in  Fig.  15, 
for  testing  the  insulation  resistance  of  a  certain  electric 
light  system.  The  resistance  of  the  voltmeter  (Vx)  connected 
in  series  with  the  resistance  to  be  measured  was  50  000  ohms. 
The  voltmeter  (Vg)  read  500  volts  and  (Vx)  10  volts.  What 
was  the  insulation  resistance  in  megohms? 

Solution. — Substituting  the  voltmeter  readings  and  the  re- 
sistance Rv  in  equation  (60)  gives 

500  —  10 
R  =  -  -  X  50  000  =  2  250  000 

10 
2  250  000  -5-  1  000  000  =  2.25 

Ans.     2.25  megohms. 

56.  Direct-Deflection  Method. — A  galvanometer  (G)  is  con- 
nected in  series  with  the  resistance  to  be  measured  and  the 
two  then  connected  to  a  source  of  e.m.f.,  as  shown  in  Fig. 
16.  The  indication  produced  on  the  galvanometer  when 
the  circuit  is  closed  should  be  noted.  The  unknown  resist- 
ance is  then  replaced  by  a  known  resistance  and  the  cir- 


ISEBiES  AND  DIVIDED  CIRCUITS 


51 


cuit  again  closed  and  the  deflection  again  noted.     The  cur- 
rent  in   the   circuit   for   the   two    cases   can    be   determined 

from  the  deflections  of  the 
galvanometer.  Let  (Rg) 
represent  the  resistance  of 


n^ 

B           ft      ^px>   AAA/»-^        battery   pressure,    (R)  the 

I I  |J  | s-^J      -  VVVW          known  resistance,  (X)  the 

unknown    resistance,  (Ir) 

Fis-  16                             the    current    through  the 

known  resistance,  and  (Ix) 
the  current  through  the  unknown  resistance,  then 


and 


Ix  = 


Ir  = 


E 


E 


(61) 


(62) 


Since  the  same  pressure  is  acting  on  the  circuit  in  both 
cases,  and  knowing  the  current  in  a  circuit  will  vary  in- 
versely as  the  resistance,  the  relation  may  be  written 

Ix       Rg  +  R 

(63) 
Ir        Rs  +  X 

Calculating  the  value  of  (X)  from  the  above  equation  we 
have 

\  Ir    (Rg   +   R) 

X  =  -  Rg  (64) 

I, 

The  resistance  of  the  galvanometer  is  usually  very  small 
in  comparison  to  the  resistance  being  measured  so  that  it  may 
be  neglected  in  the  above  equation,  which  gives 

Ir 

X  =  —  XR  (65) 


as  the  resistance  of  the   unknown   in  terms   of  the   current 
in  the  two  cases  and  the  value  of  the  known  resistance  (R). 


52  PRACTICAL  APPLIED  ELECTRICITY 

This  method  is  used  in  determining  the  insulation  of  coils  of 
wire,  etc.  The  wire  whose  insulation  is  to  be  measured  is 
immersed  in  a  salty  solution  (it  being  a  better  conductor  than 
ordinary  water),  with  at  least  three  feet  of  the  wire  out  of  the 
solution  at  each  end.  One  terminal  of  the  testing  circuit  is 
connected  to  the  wire  itself  and  the  other  terminal  to  a 
metallic  plate  placed  in  the  solution.  The  resistance  between 
the  wire  and  the  solution  is  then  measured,  giving  the  insula- 
tion resistance  for  the  length  of  wire  immersed  in  the  solution. 

The  insulation  resistance  of  a  wire  varies  inversely  as  its 
length,  because  with  an  increase  in  length  there  is  more 
surface  exposed,  resulting  in  a  greater  leakage  and  less 
resistance. 

57.  Principle  of  the  Slide-Wire  Wheatstone  Bridge.— Two 
resistances,  which  may  be  equal  or  unequal,  are  shown  con- 
nected in  parallel  between  the  points  (A)  and  (B),  Fig.  17, 
and  the  combination  is  connected  to  a  source  of  e.m.f.,  such 


AAAAAA/VWWWWWWV\V 


Fig.  17 

as  the  battery  (B).  The  drop  in  potential  across  the  two 
branches  of  the  divided  circuit  is  the  same  regardless  of  the 
relation  of  the  two  resistances.  If  the  resistance  in  each 
branch  is  the  same,  then  the  drop  over  a  certain  resistance  in 
one  branch  is  equal  to  the  drop  over  the  same  resistance  in 
the  other  branch.  When  the  resistances  of  the  two  branches 
are  not  equal,  the  above  relation  does  not  hold  true,  but  there 
are  points  on  the  two  branches  that  have  the  same  potential 
with  respect  to  (A)  or  (B).  Select  some  point,  such  as  (C) 
on  the  lower  branch,  that  will  always  have  a  potential  less 
than  the  point  (A)  and  higher  than  the  point  (B)  when  the 
current  is  in  the  direction  indicated  by  the  arrows.  There  is 


SERIES  AND  DIVIDED  CIRCUITS  53 

a  point  on  the  upper  branch  whose  potential  is  equal  to  that 
of  (C)  and  this  point  can  be  located  by  means  of  a  galvanom- 
eter as  follows:  Connect  one  terminal  of  the  galvanometer  to 
the  point  (C)  and  slide  the  other  terminal  along  the  upper 
branch  until  a  point  is  found  which  results  in  no  deflection 
of  the  galvanometer  when  the  circuit  is  closed.  This  point, 
which  is  marked  (D)  in  the  figure,  is  at  the  same  potential  as 
the  point  (C),  since  there  is  no  current  between  them,  there 
being  no  deflection  produced  on  the  galvanometer. 

When  the  point  (D)  has  been  located,  the  drop  in  potential 
across  (AC)  is  equal  to  the  drop  across  (AD),  and  the 
drop  across  (CB)  is  equal  to  the  drop  across  (DB).  The 
resistance  (AC)  bears  the  same  relation  to  (AD),  after  a 
balance  is  obtained,  as  the  resistance  (C  B)  bears  to  (DB). 
This  statement  may  be  put  into  the  form  of  a  simple  equa- 
tion, thus 

Resistance   (AD)         Resistance   (DB) 

(66) 

Resistance    (AC)         Resistance    (CB) 

For  example,  suppose  the  resistance  (AC)  and  the  total 
resistance  of  the  upper  branch  are  known  and  the  resistance 
(C  B)  is  unknown.  A  balance  is  obtained,  as  previously  de- 
scribed, and,  from  the  position  of  the  point  (D)  on  the  upper 
branch,  the  values  of  the  resistances  (AD)  and  (DB)  may 
be  determined,  the  combined  resistance  of  the  two  being 
known.  The  above  equation  can  then  be  changed  to  the  form 

Res.   (DB) 
Resistance  (C  B)  =  —  -  X  Res.  (A  C)   (67) 

Res.  (AD) 

By  substituting  the  value  of  the  three  resistances  (AC), 
(DB),  and  (AD)  in  the  above  equation,  the  value  of  the 
resistance  (C  B)  may  be  determined.  This  type  of  bridge  is 
called  a  slide-wire  pattern  'because  the  upper  branch  is  usually 
a  piece  of  resistance  wire  stretched  between  the  points  (A) 
and  (B).  The  wire  is  stretched  over  a  board  divided  into 
equal  parts  and  the  relation  between  the  two  resistances 
(AD)  and  (DB)  can  be  determined  in  terms  of  their  respect- 
ive lengths,  the  resistance  of  the  wire  varying  directly  as  the 
length.  The  two  resistances  (A  D)  and  (D  B)  are  called  the 


54  PRACTICAL  APPLIED  ELECTRICITY 

ratio-arms,  since  their  relation  to  each  other  gives  the  ratio 
between  the  known  and  the  unknown  resistances. 

58.  Commercial  Wheatstone  Bridge. — The  form  of  Wheat- 
stone  bridge  described  in  the  previous  section  is  not  used 
to  any  great  extent  in  practice,  as  its  operation  is  usually  too 
tedious,  and  for  this  reason  it  is  confined  almost  entirely  to 
laboratory  work.  The  principle  of  the  commercial  bridge  is 
the  same  as  that  of  the  slide-wire  bridge,  differing  only  in 
construction  and  operation.  A  diagram  of  a  simple  form  of 


Fig.  18 


bridge  is  shown  in  Fig.  18.  The  letters  in  the  figure  corre- 
spond to  those  in  Fig.  17.  The  resistances  (DB)  and  (DA) 
are  the  ratio  arms,  consisting  of  three  coils  each,  having  the 
resistances  marked  in  the  figure.  The  resistance  (AC), 
called  the  rheostat  of  the  bridge,  consists  of  a  number  of  coils 
ranging  in  value  from  a  very  low  resistance  to  several  hun- 
dred ohms,  depending  upon  the  range  of  the  bridge.  The 
various  resistance  coils  that  form  the  different  arms  of  the 
bridge  can  be  cut  in  or  out  of  circuit  by  means  of  metallic 
plugs  that  connect  massive  brass  or  copper  strips  on  top 


SEKIES  AND  DIVIDED  CIRCUITS  55 

of  the  bridge.  When  a  certain  plug  is  removed  the  resistance 
coil  that  was  shorted  by  the  plug  is  connected  in  the  circuit. 
The  unknown  resistance  (X)  is  connected  between  the  points 
(B)  and  (C).  When  a  balance  is  obtained  on  the  galvanom- 
eter, the  following  relation  exists  between  the  various  arms  of 
the  bridge 

a       R 

(68) 

or  b        X 

b 

X  =  — R  (69) 

a 

In  making  a  measurement  with  this  form  of  bridge  the 
relation  between  the  ratio  arms  (a)  and  (b)  remains  con- 
stant after  they  are  adjusted  to  a  certain  value,  and  a  balance 
is  obtained  by  changing  the  value  of  the  resistance  in  the 
rheostat  (R).  If  (a)  and  (b)  are  made  equal,  then  the  resist- 
ance in  (R),  when  a  balance  is  obtained,  is  equal  to  the 
resistance  of  the  unknown  (X).  When  it  is  desired  to  measure 
a  resistance  larger  than  the  value  of  (R),  make  the  ratio  arm 


Fig.  19 


(b)  greater  than  (a);  and  to  measure  a  resistance  smaller 
than  (R),  make  (b)  less  than  (a).  In  the  first  case  the  resist- 
ance (R)  is  multiplied  by  a  certain  number,  which  is  the 
quotient  of  (b-=-a),  and  will  always  be  greater  than  unity 
to  obtain  the  value  of  (X) ;  and  in  the  second  case  (R)  will 
be  multiplied  by  a  number  less  than  unity.  The  galvonometer 


56 


PRACTICAL  APPLIED  ELECTRICITY 


and  the  battery  connections  may  be  interchanged  without 
interfering  with  the  operation  of  the  bridge. 

There  are  a  large  number  of  different  forms  of  bridges  on 
the  market  at  the  present  time.  Some  of  them  have  the  gal- 
vanometer, battery,  and  contact  keys  all  mounted  in  the  same 
box  with  the  resistances,  and  the  only  connection  that  must  be 
made  is  to  the  resistance  to  be  measured.  Fig.  19  shows  a 
good  form  of  portable  Wheatstone  bridge. 

59.  The  Ohmmeter. — An  Ohmmeter  is  an  instrument  for 
measuring  automatically  the  resistance  of  a  circuit  connected 
to  its  terminals,  by  noting  the  position  of  a  pointer  on  a  dial 
that  is  marked  to  read  directly  in  ohms.  The  principle  of 
the  Evershed  instrument  is  as  follows:  The  deflecting  sys- 
tem consists  of  a  set  of  coils  (BB^,  as  shown  in  Fig.  20, 
rigidly  fastened  together,  which  move  about  a  center  (O)  in 
the  magnetic  field  of  strong  permanent  magnets  (MM).  The 
nature  of  this  construction  brings  the  instrument  into  the 
class  of  moving-coil  permanent-magnet  instruments,  the  ad- 
vantages of  which  for  reliability,  accuracy  under  all  condi- 
tions of  use,  and  promptness  in  taking  deflection,  are  quite 


Fig.  20 


numerous.  Springs  are  not  used  for  the  control  of  the  moving 
system,  so  that  when  not  in  use  the  needle  may  stand  at  any 
point  along  the  scale. 

If  the  generator  is  set  in  motion  and  no  resistance  is  con- 
nected between  the  external  terminals,  current  exists  only  in 
the  coils  (BBj),  which  move  at  once  to  such  location  that  (B) 
is  clear  of  the  horn  on  the  pole  piece  and  (B^  is  central 
over  the  air  gap  in  the  (O)  shaped  centrally  placed  hollow 


SERIES  AND  DIVIDED  CIRCUITS  57 

iron  cylinder.  The  needle  then  stands  over  Inf.  on  the  scale, 
showing  an  infinite  resistance  between  the  terminals.  If  a 
measurable  resistance  is  connected  between  the  terminals, 
a  current  exists  in  the  stationary  coil  and,  due  to  the  thrust 
experienced  by  it  in  the  magnetic  field,  the  needle  moves  along 
the  scale,  and  a  direct  reading  of  the  amount  of  resistance 
so  connected  is  made. 

The  hand  dynamo  (D)  operates  in  the  field  of  the  same  per- 
manent magnets.  The  armature  is  wound  so  that  a  rated 
e.m.f.  of  125,  250,  500,  or  even  1000  volts  are  generated  for 
some  100  r.p.m.  of  the  crank.  The  design  of  this  machine 
is  the  result  of  a  large  amount  of  research  by  Mr.  Evershed, 
in  his  desire  to  make  a  rugged,  reliable,  light-weight  gen- 
erator which  would  require  slight  propelling  force  to  drive  it. 

Instruments  of  this  kind  are  usually  used  in  measuring  very 
high  resistances,  such  as  insulation  resistances,  etc. 


CHAPTER  IV 


PRIMARY    BATTERIES 


60.  The  Voltaic  Cell. — If  two  unlike  metals  are  immersed 
in  a  solution,  which  is  capable  of  acting  upon  one  of  them 
more  than  upon  the  other,  there  will  be  a  current  of  elec- 
tricity between  them  when  they  are  connected  by  a  wire. 
Such  a  combination  constitutes  a  voltaic  cell.  This  cell  was 
first  discovered  by  an  Italian  physicist,  Volta,  in  1800,  and 
Was  named  after  him.  It  is,  however,  often  called  a  gal- 
vanic cell,  after  Galvani,  who  was  Volta's  contemporary. 

61.  Simple  Voltaic  Cell.  —  Two 
pieces  of  metal,  such  as  copper  and 
zinc,  immersed  in  a  solution  that  con- 
tains a  little  sulphuric  acid,  or  other 
oxidizing  acid,  forms  a  simple  voltaic 
cell.  Such  a  cell  is  shown  in  Fig.  21. 
This  cell  is  capable  of  furnishing  a 
continuous  flow  of  electricity  through 
a  wire  whose  ends  are  brought  into 
contact  with  the  strips  of  copper 
and  zinc.  When  the  electricity  flows, 
the  zinc  is  wasted  away,  its  con- 
sumption furnishing  the  energy  re- 
quired to  drive  the  current  through 
the  cell  and  the  connecting  wire. 
The  cell  might  be  thought  of  then 

as  a  chemical  furnace  in  which  the  fuel  is  zinc.  The  copper 
strip  from  which  the  flow  starts  in  passing  through  the 
external  circuit  is  called  the  positive  pole  of  the  battery,  and 
the  zinc  sirip  is  called  the  negative  pole.  These  poles  are 
usually  designated  by  the  plus  (  +  )  and  negative  ( — )  signs. 

58 


Fig.  21 


PKIMABY  BATTEEIES 


59 


!t  is  the  difference  in  electrical  pressure  between  the  positive 
and  the  negative  poles  of  the  battery  that  causes  a  current  in 
the  circuit  when  the  poles  are  connected. 

62.  Voltaic  Battery. — If  a  number  of  voltaic  cells  are  joined 
in  series — the  zinc  plate  of  one  joined  to  the  copper  plate  of 
the  next,  and  so  on — a  greater  difference  in  electrical  pressure 
will  be  produced  between  the  copper  pole  at  one  end  and 
the  zinc  pole  at  the  other  end.  When  the  poles  forming 
the  terminals  of  such  a  series  are  joined,  there  will  be  a  more 
powerful  current  than  one  cell  would  cause.  [It  is  assumed 
that  the  resistance  01  the  circuit  connecting  the  two  poles  or 
terminals  is  practically  the  same  as  the  resistance  of  the  cir- 
cuit connecting  the  terminals  of  a  single  cell.]  Such  a  group- 
ing of  voltaic  cells  is  called  a  voltaic  battery.  Four  single  cells 
(Ci),  (C2),  (C3),  and  (C4),  are  shown  connected  in  series  in 
Fig.  22.  The  cells  may  be  combined  in  other  ways  and  these 


ZCZCZCZC 


Fig.  22 


c, 


methods  will  be  taken  up  later.  It  is  customary  to  represent 
a  single  cell  by  two  parallel  lines,  as  shown  in  Fig.  23, 
instead  of  drawing  a  picture  of  the  cell  each  time  you  want  to 
show  it  in  a  diagram.  The  long  line  corresponds  to  the  plus 
(  +  ),  or  positive,  terminal,  and  the  short  line  corresponds  to 
the  minus  ( — ),  or  negative,  terminal. 

63.  Chemical  Action  in  a  Battery. — A  continuous  potential 
difference  is  maintained  between  the  zinc  and  copper  in  a 
simple  voltaic  cell  chiefly  by  the  action  of  the  exciting  liquid, 
say  sulphuric  acid,  upon  the  zinc.  Sulphuric  acid  is  a  complex 
substance  in  which  every  molecule  is  made  up  of  a  group  of 
atoms,  2  of  hydrogen,  1  of  sulphur,  and  4  of  oxygen;  or  in 
symbols  H2SO4.  The  SO4  part  of  the  acid  has  a  very  strong 
affinity  for  the  zinc,  and  attacks  it,  when  the  plates  are  con- 
nected, producing  a  current,  and  forms  zinc  sulphate  ZnSO4, 
which  is  dissolved  in  the  water.  There  will  be  two  parts  of 


60  PRACTICAL  APPLIED  ELECTKICITY 

hydrogen  gas  liberated  for  every  portion  of  the  SO4  part  of 
the  sulphuric  acid  that  unites  with  the  zinc.  The  zinc  thus 
replaces  the  hydrogen  in  the  acid,  when  the  cell  is  being 
used,  setting  the  hydrogen  free.  This  chemical  reaction  is 
expressed  in  the  equation 

Zn     +       H2SO4  ZnSO4          +          H2 

Zinc  and  sulphuric  acid  produce  zinc  sulphate  and  hydrogen. 

This  chemical  action  continues  as  long  as  the  battery  is  sup- 
plying a  current,  the  zinc  gradually  wasting  away  and  the 
power  of  the  acid  to  attack  the  zinc  gradually  becoming 
exhausted.  Electrical  energy  is  thus  supplied  to  the  external 
circuit  by  the  combination  of  zinc  and  acid  inside  the  cell. 

64.  Local    Action. — When  the  circuit  of  a   battery  is   not 
closed,  the  current  cannot  exist,  and  there  should  be  no  chem- 
ical action  as  long  as  the  battery  is  producing  no  current. 
Ordinary  commercial  zinc,  however,  contains  many  impurities, 
such  as  tin,  arsenic,  iron,  lead,  carbon,  etc.,  and  these  numer- 
ous foreign  particles  form  local  voltaic  cells  on  the  surface  of 
the  zinc  inside  the  cell,  with  the  result  that  the  zinc  is  being 
continuously  eaten  away  whether  the  cell  is  supplying  current 
to  an  external  circuit  or  at  rest.   These  small  cells  weaken  the 
current  the  main  cell  is  capable  of  supplying  under  proper 
conditions.     Often  local  action  is  caused  by  a  difference  in 
density   of  the   liquid   at   different   parts   of   the   cell.     This 
causes  the  zinc  at  the  top  of  the  cell  to  waste  away  and  it 
may  be  entirely  eaten  off. 

65.  Amalgamation. — To  do  away  with  this  local  action,  and 
thus  abolish  the  wasting  of  the  zinc  while  the  battery  is  at 
rest,  it  is  usual  to  amalgamate  the  surface  of  the  zinc  plates 
with  mercury.    The  surface  to  be  amalgamated  should  be  thor- 
oughly cleaned  by  dipping  it  into  acid  and  then  a  few  drops  of 
mercury  should   be  rubbed   into   the  surface.     The  mercury 
unites  with  the  zinc  at  the  surface  forming  pasty  amalgam. 
The  foreign  particles  do  not  dissolve  in  the  mercury,  but  float 
to  the  surface,  and  they  are  carried  away  by  the  hydrogen  bub- 
bles.    As  the  zinc  in  the  pasty  amalgam  dissolves  into  the 
acid,  the  film  of  mercury  unites  with  fresh  portions  of  zinc, 
and  a  clean,  bright  surface  is  always  presented  to  the  liquid. 

66.  Polarization. — When  there  is  a  current  through  a  cell, 
the  hydrogen  that  is  liberated  from  the  acid  appears  upon 


PRIMARY  BATTERIES  61 

the  surface  of  the  copper,  and  the  copper  plate  becomes  prac- 
tically a  hydrogen  plate.  If  a  cell  were  made  having  a  hydro- 
gen and  zinc  plate,  there  would  be  a  current  from  the  hydro- 
gen to  the  zinc  inside  the  cell  and  from  the  zinc  to  the  hy- 
drogen outside  the  cell.  The  hydrogen  collecting  on  the  copper 
plate  tends  to  send  a  current  through  the  cell  opposite  to  that 
produced  by  the  copper  and  zinc  current.  This  results  in  the 
current  supplied  by  the  battery  decreasing  as  the  hydrogen 
on  the  copper  plate  increases,  or  the  plate  becomes  more 
nearly  covered  with  the  hydrogen  gas.  A  cell  that  has  become 
weakened  in  this  way  is  said  to  be  polarized,  and  the  phe- 
nomenon is  called  polarization.  Hence,  polarization  is  an  evil, 
and  if  it  could  be  overcome  by  preventing  the  hydrogen  bub- 
bles collecting  on  the  copper  plate,  the  cell  would  be  capable 
of  supplying  a  current  of  almost  constant  strength  as  long  as 
zinc  remained  to  be  acted  upon  and  the  acid  was  not  ex- 
hausted. Various  attempts  to  prevent  polarization  have  given 
rise  to  many  different  types  of  cells  on  the  market  at  the 
present  time. 

67.  Prevention  of  Polarization. — Various  remedies  have 
been  practiced  to  reduce  or  prevent  the  polarization  of  cells. 
These  may  be  classed  as  mechanical,  chemical,  and  electro- 
chemical. 

(a)  Mechanical    Means. — If  the  hydrogen  bubbles  be  sim- 
ply brushed  away  from  the  surface  of  the  positive  pole,  the 
resistance  they  cause  will  be  diminished.     If  air  be  blown 
into  the   acid   solution   through  a   tube,   or   if  the   liquid   be 
agitated  or  kept  in  constant  circulation  by  syphons,  the  re- 
sistance is  also  diminished.     If  the  surface  be  rough  or  cov- 
ered   with    points,   the    bubbles    collect   more    freely    at    the 
points   and   are   quickly   carried   up   to   the    surface   and   got 
rid  of.     This  remedy  is  used  in  the   Smee   cell,  which   con- 
sists  of   a   zinc    and    a    platinized    silver    plate    dipping   into 
dilute    sulphuric    acid;    the    silver    plate,    having    its    surface 
thus  covered  with  a  rough  coat  of  finely  divided  platinum, 
gives  up  the  hydrogen  bubbles  freely,  nevertheless  in  a  bat- 
tery of  Smee  Cells  the  current  falls  off  greatly  after  a  few 
minutes. 

(b)  Chemical    Means. — If   a    strongly    oxidizing    substance 
be  placed  in  the  solution  it  will  combine  with  the  hydrogen 
and  thus  will  prevent  both  the  increase  in  internal  resistance 


62  PBACTJCAL  APPLIED  ELECTEICITY 

and  the  opposing  electromotive  force.  Such  substances  are 
bichromate  of  potash,  nitric  acid,  and  bleaching  powder  (so- 
called  chloride  of  lime).  These  substances,  however,  would 
attack  the  copper  in  the  zinc-copper  cell.  Hence,  they  can 
only  be  used  in  a  zinc-carbon  or  zinc-platinum  cell. 

(c)  Electro-chemical  Means. — It  is  possible  by  employing 
double  cells  to  so  arrange  matters  that  some  solid  metal,  such 
as  copper,  shall  be  liberated,  instead  of  hydrogen  bubbles, 
at  the  point  where  the  current  leaves  the  liquid.  This  elec- 
tro-chemical exchange  entirely  obviates  polarization. 

68.  Internal  Resistance. — The  resistance  offered  by  a  cell 
to  a  current  through  it  from  one  plate  to  the  other  is  called 
its  internal  resistance.  The  value  of  the  internal  resistance 
of  any  cell  will  depend  upon  the  area  of  the  two  plates,  the 
distance  between  the  two  plates,  the  specific  resistance  of 
the  liquid,  and  the  degree  of  polarization.  As  the  polariza- 
tion of  a  cell  increases,  the  internal  resistance  increases, 
since  the  effective  area  of  the  plates  exposed  to  the  action 
of  the  liquid  is  decreased  due  to  the  accumulation  of  the 
hydrogen  gas.  This  increase  in  internal  resistance  of  a  cell 
causes  the  difference  in  potential  between  its  terminals  to 
decrease,  as  a  larger  part  of  the  electromotive  force  of  the 
cell  is  required  to  force  the  current  through  its  own  resist- 
ance and  the  available  electrical  pressure  is  decreased. 
.  69.  Factors  Determining  the  Electromotive  Force  of  a  Cell. 
— When  two  plates  of  the  same  material,  such  as  zinc,  are 
immersed  in  an  acid  solution  and  are  connected  by  a 
wire,  there  will  be  no  current  in  the  wire,  because  there  is 
a  tendency  to  opposite  currents  and  these  two  tendencies 
neutralize  each  other.  In  other  words,  the  difference  in  elec- 
trical potential  between  one  zinc  plate  and  the  solution  is 
the  same  as  that  between  the  other  zinc  plate  and  the  solu- 
tion, and  these  two  potentials  are  opposite  in  direction — when 
the  two  plates  are  connected  by  a  conductor — which  results  in 
no  current  through  the  circuit  when  it  is  closed.  The  essential 
parts  of  any  cell,  therefore,  are  two  dissimilar  materials 
immersed  in  a  solution,  one  of  which  is  more  readily  acted 
upon  by  the  solution  than  the  other.  The  greater  this 
difference  in  intensity  in  chemical  action,  the  greater  the 
difference  in  potential  between  the  terminals  of  the  cell. 

Copper,    platinum,    silver,    and    zinc    are    the    only    metals 


PEIMAKY  BATTEEIES  63 

that  have  been  mentioned  up  to  the  present  time,  but  other 
metals  may  be  used,  and  since  the  intensity  of  chemical 
action  will  be  different  for  different  metals,  there  will  be 
combinations  that  will  produce  better  results  than  others. 
For  example,  a  cell  composed  •  of  zinc  and  tin  would  not 
produce  as  large  an  electromotive  force  as  one  composed 
of  zinc  and  copper  the  same  size,  because  there  is  a  greater 
difference  of  electrical  potential  between  the  zinc  and  the 
copper  than  there  is  between  the  zinc  and  the  tin. 

The  solution  used  in  the  cell  also  determines  the  value 
of  the  difference  in  potential  between  any  combination  of 
plates.  There  will  be  a  different  value  for  the  potential 
difference  between  any  two  plates  when  they  are  immersed 
in  different  liquids. 

When  the  same  kinds  of  metals  and  solution  are  used,  the 
potential  difference  between  the  plates  will  be  the  same, 
regardless  of  the  areas  of  the  plates.  A  small  battery  will 
have  the  same  electromotive  force  as  a  large  one  composed 
of  the  same  materials. 

In  the  following  list,  the  substances  are  arranged  in  order 
depending  upon  the  degree  of  chemical  action  when  placed 
in  dilute  sulphuric  acid:  Zinc,  Iron,  Tin,  Lead,  Copper, 
Silver,  Platinum,  and  Carbon. 

70.  Classification  of  Cells. — (a)  If  a  cell  is  capable  of 
producing  a  current  directly  from  the  consumption  in  it  of 
some  substance,  such  as  zinc,  it  is  a  primary  cell.  If,  how- 
ever, a  current  must  first  be  sent  through  the  cell  to  bring 
it  to  such  a  condition  that  it  is  capable  of  producing  a  cur- 
rent, it  is  called  a  secondary,  or  storage,  cell.  The  funda- 
mental distinction  then  between  a  primary  and  a  secondary, 
or  storage,  cell  is  that,  with  the  latter  type  the  chemical 
changes  are  reversible,  while  with  the  former  type  this  is  not 
practical  even  when  possible.  The  discussion  of  the  storage 
cell  will  be  taken  up  in  a  later  chapter. 

(b)  Cells  are  also  classified  into  closed-  and  open-circuit 
types,  depending  upon  whether  they  are  or  are  not  capable 
of  furnishing  a  current  continuously.  This  classification  is 
entirely  dependent  upon  the  polarization — the  cell  which 
does  not  polarize  being  able  to  maintain  its  current  until 
its  chemical  substances  are  exhausted. 

The  Grenet  and  the  Leclanche  are  perhaps  the  best  exam- 


64 


PKACTICAL  APPLIED  ELECTRICITY 


pies  of  the  open-circuit  cells,  while  the  Daniell,  the  Lalande, 
and  the  Fuller  are  good  examples  of  the  closed-circuit  cell. 

(c)  All  cells  must  be  made  up  of  two  substances  im- 
mersed in  a  liquid,  but  in  some  cases  there  are  different 
liquids  separated  by  gravity  or  a  porous  cup.  Cells  may  then 
be  classified,  as  to  their  construction,  into  single-fluid  cells 
and  double-fluid  cells.  The  Grenet,  Leclanche,  and  Lalande 
are  good  examples  of  single-fluid  cells,  while  the  Bunsen, 
Fuller,  Daniell,  and  Grove  are  perhaps  the  best  examples 
of  the  double-fluid  type. 

71.  Forms  of  Primary  Cells. — The  various  cells  given  in 
Table  No.  V  are  the  principal  ones  that  are  used  to  any 
extent  and  the  construction  of  a  few  of  these  will  be  given  in 
detail  in  the  following  sections. 

TABLE  NO.  V 
PRIMARY    CELLS 


Names  of 
Cell 

Negative 
Pole 

Positive 
Pole 

Solution 

Depolariz- 
ing Agent 

E.M.F. 
in 
Volts 

Internal 
Resistance 
in  Ohms 

Smee  

Zinc 

Platinized 

Solution  of 

None 

.65 

0.5 

Silver 

Sulphuric 
Acid 

Grenet  — 

Zinc 

Graphite 
(Carbon) 

Solution  of 
Sulphuric 
Acid 

Potassium 
Bichro- 
mate 

2.1 

2  to  .5 

Leclanche. 

Zinc 

Graphite 
(Carbon) 

Ammoni'm 
Chloride 

Manganese 
Dioxide 

.5  to 

1.6 

1.5 

Daniell.... 

Zinc 

Copper 

Zinc  Sul- 
phate 

Copper 
Sulphate 

1.079 

2  to  6 

Lalande... 

Zinc 

Graphite 
(Carbon) 

Caustic 
Potash  or 
Potassium 
Hydrate 

Cupric 
Oxide 

0.8  to 
0.9 

1.3 

Fuller  

Zinc 

Graphite 
(Carbon) 

Sulphuric 
Acid 

Potassium 
Bichro- 
mate 

2.0 

0.5  to  0.7 

Bunsen..  .. 

Zinc 

Graphite 
(Carbon) 

Dilute 
Sulphuric 
Acid 

Nitric 
Acid 

1.8  to 
1.98 

.08  to.  11 

Grove  

Clark 
Standard,. 

Zinc 
Zinc 

Platinum 
Mercury 

Dilute 
Sulphuric 
Acid 

Zinc 
Sulphate 

Nitric 
Acid 

Mercurous 
Sulphate 

1.96 
1.434 

.lto.12 
.3  to  .5 

Weston.... 

Cadmium 

Mercury 

Cadmium 
Sulphate 

Mercurous 
Sulphate 

1.01830 

PRIMARY  BATTERIES  65 

72.  Chemicals  Used  in  Cells  and  Their  Symbols. — 

Sulphuric  Acid,  H2SO4. 

Chromic  Acid,  CrO3. 

Manganese  Dioxide,   MnO. 

Zinc    Chloride,    ZnCl2. 

Lead  Oxide,  PbO. 

Zinc  Sulphate,  ZnSO4. 

Nitric  Acid,  HNO3. 

Hydrochloric  Acid,  HC1. 

Silver  Chloride,  AgCl. 

Copper  Oxide,  CuO. 

Lead   Peroxide,    PbO2. 

Sodium  Chloride,  NaCl. 

Caustic  Potash  or  Potassium  Hydrate,  KOH. 

Copper  Sulphate  (blue  vitriol),  CuSO4. 

Zinc   Sulphate    (white   vitriol),   ZnSO4. 

Ammonium   Chloride    (sal-ammoniac),  NH4C1. 

Bichromate  of  Potassium,  K2Cr2O7. 

Bichromate  of  Soda,  Na2Cr2O7. 

Mercurous   Sulphate,   Hg2SO4. 

Cadmium  Sulphate,   CdSO4. 

73.  Mechanical    Depolarization. — The   Smee  cell  has  been 
mentioned  in  section  (67)  as  a  good  example  of  a  mechanical 
means  of  preventing  polarization.     This  cell  was  used  com- 
mercially a  number  of  years  ago,  but  it  was  not  very  suc- 
cessful.    A  Smee  cell  is  shown  in  Fig.  24. 

There  are  a  number  of  cells  used  for  intermittent  work, 
such  as  ringing  door  bells,  that  depend  entirely  upon  the 
use  of  a  large  positive  plate  surface  to  lessen  the  rapidity 
of  polarization.  They  consist  usually  of  zinc  and  carbon 
plates  immersed  in  a  solution  of  sal  ammoniac  (ammonium 
chloride),  see  section  (72).  The  carbons  for  such  cells  are 
made  in  almost  endless  variety  and  with  very  large  surface. 

74.  Chemical     Depolarization.  —  Bichromate    Cells. — There 
are   a   number   of    different   forms    of   bichromate    cells,   the 
principal  ones  of  which  are  perhaps  the  Grenet  and  Fuller. 

(a)  Grenet  Cell. — In  this  form  a  zinc  plate  is  suspended 
by  a  rod  between  two  carbon  plates,  see  Fig.  25,  so  that 
it  does  not  touch  them,  and  when  the  cell  is  not  in  use  the 
zinc  can  be  removed  from  the  solution  by  raising  and  fasten- 


66 


PRACTICAL  APPLIED  ELECTRICITY 


ing  the  rod  by  means  of  a  set  screw,  as  the  acid  acts  on 
the  zinc  when  the  cell  is  not  in  use.  Sulphuric  acid  and 
water  is  the  solution  used  in  this  cell,  to  which  is  added 
potassium  bichromate  that  acts  as  the  depolarizer.  The 
bichromate  is  rich  in  oxygen,  which  readily  combines  with 
the  liberated  hydrogen  and  thus  prevents  polarization.  This 


Fig.  24 


Fig. 


cell  gives  a  large  e.m.f.  and  is  capable  of  supplying  a 
strong  current  for  a  short  time,  but  the  liquid  soon  becomes 
exhausted. 

(b)  Fuller  Cell. — This  form  of  bichromate  cell  is  a  double 
fluid  type,  and  has  the  advantage  over  the  Grenet  type  in 
that  the  zinc  is  always  kept  well  amalgamated  and  it  is  not 
necessary  to  remove  it  from  the  solution.  A  pyramidal  block 
of  zinc  is  placed  in  a.  small  porous  cup;  Fig.  26,  and  a 
small  quantity  of  mercury  poured  in.  The  cup  is  then  filled 
with  a  diluted  solution  of  sulphuric  acid  and  placed  in  a 
glass  jar  containing  a  solution  of  potassium  bichromate 
and  the  carbon  plate  (P).  A  conductor,  covered  with  a  suit- 
able insulation,  is  attached  to  the  block  of  zinc  and  serves  as 
one  terminal  of  the  cell.  The  zinc  is  well  amalgamated  by 
the  mercury  and  there  is  practically  no  local  action.  The 


PKIMAKY  BATTERIES 


67 


cell  gives  a  large  e.m.f.  and  may  be  used  for  open  circuit 
or   semi-closed   circuit   work. 

75.  Chemical  Depolarization. — Leclanche. — This  cell  con- 
sists of  a  zinc  plate  in  a  solution  of  ammonium  chloride  and 
a  carbon  plate  placed  inside  a  porous  cup  which  is  packed 
full  of  manganese  dioxide  and  powdered  carbon.  The  action 
of  the  manganese  dioxide  on  the  hydrogen  is  not  quick 
enough  to  prevent  polarization  entirely  when  large  currents 


Zinc 


Fig.  26 


Fig.  27 


are  taken  from  the  cell.  The  cell,  however,  will  recover 
when  allowed  to  stand  on  open  circuit.  A  great  advantage  of 
this  type  of  cell  lies  in  the  fact  that  the  zinc  is  not  acted 
on  at  all  by  the  ammonium  chloride  when  the  cell  is  on 
open  circuit,  and  as  a  result  it  can  be  left  for  almost  an 
indefinite  period  when  the  circuit  is  open  without  deteriora- 
tion. These  cells  are  usually  used  for  intermittent  work, 
such  as  ringing  door  bells,  and  will  supply  quite  a  large 
current  for  a  short  time.  Their  e.m.f.  is  about  1.5  volts. 
Leclanche  cells  are  called  open-circuit  cells  on  account  of 
the  very  slight  chemical  action  that  takes  place  when  the 
circuit  is  open.  A  Leclanche  cell  is  shown  in  Fig.  27. 

76.  Electro-Chemical  Depolarization. — Daniel!  Cells. — This 
type  of  cell  consists  of  a  zinc  plate  immersed  in  a  solu- 
tion of  zinc  sulphate  and  a  copper  plate  immersed  in  a 


68 


PRACTICAL  APPLIED  ELECTRICITY 


solution  of  copper  sulphate.  The  two  liquids  may  be  kept 
apart  either  by  gravity  or  by  a  porous  earthen  cup,  as  shown 
in  Fig.  28.  When  the  solutions  are  kept  separated  by  grav- 
ity, the  cell  is  called  the  gravity,  or  crowfoot  type.  A  cross- 
section  of  a  Daniell  cell,  in  which  the  liquids  are  separated 
by  a  porous  cup,  is  shown  in  Fig.  29.  The  gravity  cell  is 


"t*         PorousCup       — 


Fig.   28 


Fig.  29 


shown  in  Fig.  30.  The  copper  sulphate  being  the  heavier 
of  the  two  liquids  remains  at  the  bottom  about  the  plate 
of  copper,  while  the  zinc  sulphate  remains  at  the  top  about 
the  zinc  plate.  This  cell  will  give  a  very  constant  e.m.f.  of 
about  1.08  volts.  It  has  a  large  internal  resistance  (two 
to  six  ohms)  and  as  a  result  is  not  capable  of  supplying 
a  very  large  current.  The  current  supplied,  however,  is  con- 
stant, and  it  will  operate  for  a  great  length  of  time  without 
renewal. 

The  Daniell  cell  is  a  closed-circuit  cell  and  it  should 
never  be  allowed  to  stand  on  open  circuit,  but  a  resistance 
(thirty  to  fifty  ohms)  should  always  be  connected  across 
its  terminals. 

77.  Dry  Cells. — The  dry  cell  is  a  special  form  of  the 
Leclanche  cell  first  described.  The  cell  is  not  altogether 
dry,  since  the  zinc  and  carbon  plates  are  placed  in  a  moist 
paste  which  consists  usually  of  .  ammonium  chloride,  one 
part;  plaster  of  Paris,  three  parts;  zinc  chloride,  one  part; 


PRIMARY  BATTERIES  69 

zinc  oxide,  one  part,  and  sawdust.  These  various  materials*, 
composing  the  above  mixture  are  thoroughly  mixed  and  then 
moistened  with  a  small  quantity  of  water.  The  paste  thus 
formed  is  packed  around  a  carbon  rod,  placed  inside  a  zinc 
cup  lined  with  moistened  blotting  paper,  and  the  cup  is  sealed 
with  some  kind  of  wax  to  prevent  evaporation.  There  are  a 
large  number  of  different  makes  of  dry  cells  on  the  market 
at  the  present  time  but  the  chemical  action  in  each  is  prac- 
tically the  same.  The  dry  cell  is  a  very  convenient  form 
of  cell  and  its  operation  is  very  satisfactory  for  work  requir- 
ing an  intermittent  current.  Fig.  31  shows  a  cross-section 
through  a  dry  cell. 


Paste  Board 
Covering 

Pitch 
; — Zinc  Cup 

filling 

Carbon 
—  Blotting 
Paper 


Fig.   30 


Fig.   31 


78.  Standard  Cells. — A  standard  cell  is  one  whose  e.m.f. 
can  be  accurately  calculated  and  will  remain  constant.  The 
Clark  Standard  cell  and  the  Weston  cell  are  the  two  best 
examples  of  standard  cells.  The  Clark  cell  has  an  e.m.f.  of 
1.434  volts  at  15° C.  and  a  correction  must  be  made  in  this 
value  when  the  cell  is  used  at  some  other  temperature. 

The  Weston  normal  cell  has  an  e.m.f.  of  1.01830  volts  and 
there  is  practically  no  change  in  its  e.m.f.  due  to  a  change 
in  temperature.  A  Weston  standard  cell,  as  manufactured  by 
the  Weston  Electrical  Instrument  Company,  is  shown  in 
Fig.  32.  The  e.m.f.  of  different  Weston  cells  is  not  exactly 
the  same,  but  they  are  standardized  in  the  factory  and  a 
certificate  accompanies  each  cell.  The  average  e.m.f.  of  a 


70  PRACTICAL  APPLIED  ELECTK1CITY 

number  of  cells  tested  by  the  Bureau  of  Standards  at  Wash- 
ington, D.  C.,  was  1.01869  volts. 

A  great  amount  of  care  is  exercised  in  assembling  standard 
cells,  to  see  that  the  materials  used  are  the  very  best  and 
that  they  are  all  constructed  alike. 

79.  Requirements  of  Good  Cell. 
— A  good  cell  should  fulfill  all,  or 
the  greater  part,  of  the  following 
conditions: 

(a)  Its      electromotive      force 
should  be  high  and  constant. 

(b)  Its  internal  resistance  should 
be  small. 

(c)  It  should  be  capable  of  sup- 
plying    a     constant     current,     and, 
therefore,  entirely  free  from  polari- 
zation,   and     not    liable    to    rapid 

32  exhaustion,    requiring    frequent    re- 

newals of  the  liquid  or  plates. 

(d)  It  should  be  free  from  local  action. 

(e)  It  should  be  cheap   and  of  durable   materials   which 
results  in  a  low  cost  for  renewals  when  they  are  required. 

(f)  It  should  be  easily  managed,  and,  if  possible,  should 
not  emit  corrosive  fumes. 

No  particular  cell  fulfills  all  of  the  above  conditions,  how- 
ever, and  some  cells  are  better  for  one  purpose  than  others. 
Thus,  for  telegraph  work  over  a  long  line,  a  cell  of  consid- 
erable internal  resistance  is  no  great  disadvantage;  while  a 
large  internal  resistance  is  a  great  disadvantage  when  the 
cell  is  supplying  current  to  a  circuit  of  corresponding  low 
resistance.  An  open-circuit  cell  would  not  operate  satisfac- 
torily in  driving  a  small  motor,  but  would  be  quite  satisfac- 
tory for  intermittent  work;  while  the  closed-circuit  type 
would  be  very  unsatisfactory  for  intermittent  work. 

80.  Series  Connection  of  Cells. — Any  number  of  cells  are 
said  to  be  connected  in  series  when  the  positive  terminal 
of  one  is  connected  to  the  negative  terminal  of  another, 
and  so  on.  When  all  of  the  cells  are  connected,  there  remains 
a  positive  and  a  negative  terminal  which  form  the  terminals 
of  the  battery.  If  (n)  cells  are  connected  in  series,  as  shown 
in  Fig.  33,  and  they  each  have  an  e.m.f.  of  (e)  volts,  the 


PRIMARY  BATTERIES 


71 


combination  will  have  an  e.m.f.  of  (ne)  volts.  The  internal 
resistance  of  the  battery  will  be  equal  to  (nr)  ohms  where 
(r)  is  the  internal  resistance  of  each  cell.  If  the  external 
resistance  or  the  resistance  of  the  circuit  to  which  the  battery 
is  connected  is  (R)  ohms,  then  the  current  produced  by  the 
combination  will  be 

ne 

1  = (70) 

R-f-nr 

In  the  above  equation  (R  +  nr)  represents  the  total  resist- 
ance of  the  entire  circuit  and    (ne)   the  total  electromotive 


Fig.  34 


force  acting  in  the  circuit.  Fig.  33  sho\\rf  three  cells  con- 
nected in  series  and  the  battery  thus  formed  connected  to 
a  resistance  (R). 

Fig.  34  shows  a  hydraulic  analogy  similar  to  the  connection 
of  cells  in  series.  The  pumps  (Pi)  and  (P2)  are  so  arranged 
that  their  pressures  are  added,  the  total  pressure  acting  in 
the  circuit  being  equal  to  the  sum  of  the  pressures  produced 
by  the  respective  pumps.  If  there  is  no  water  flowing  and 
the  gauge  (G^  reads  zero,  then  (G2)  reads  the  pressure 
produced  by  the  pump  (Pj).  The  difference  in  the  readings 
of  (G3)  and  (G2)  is  the  pressure  produced  by  the  pump 
(P2).  Hence  (G3)  reads  the  total  pressure  produced  by  the 
two  pumps  combined  when  (Gi)  reads  zero  and  no  water  is 
flowing.  When  there  is  a  flow  of  water,  however,  part  of  the 
pressure  produced  by  the  pumps  is  used  in  causing  the  water 
to  pass  through  them  or  to  overcome  their  internal  resistance, 
and  as  a  result  the  indication  on  (G;})  is  reduced. 

Example. — Six  cells  having  an  e.m.f.  of  1.5  volts  each  and 
an  internal  resistance  of  .6  ohm  each  are  connected  in  series 


72  PRACTICAL  APPLIED  ELECTRICITY 

with    a    resistance    of    10    ohms.    -What    is    the    current    in 
the  resistance  when  the  circuit  is  closed? 

Solution. — By  a  direct  substitution  in  equation  (70)  we 
have 

6  X  1.5  9  9 

I  =  =  6.62— 

10  +  (6  X  .6)         10  +  3.6        13.6 

Ans.     6.62  amperes. 

81.  Parallel  Connection  of  Cells. — When  (n)  cells,  all 
having  the  same  e.m.f.,  are  all  connected  in  parallel,  then 
the  e.m.f.  of  the  combination  is  only  that  of  a  single  cell. 
The  internal  resistance  of  a  battery  formed  of  a  number  of 
cells  connected  in  parallel  is  less  than  the  internal  resistance 


I — vwww — i 


Fig.  35 


Fig.  36 


of  a  single  cell.    If  (r)  is  the  internal  resistance  of  each  cell, 
and  there  are   (n)    cells  in  parallel,  then  the  total  internal 


resistance  will  be  \^~J.  If  the  resistance  of  the  external 
circuit  is  (R)  ohms,  then  the  current  produced  by  the  com- 
bination will  be 


r 

R  +  - 
n 


(71) 


In  the  above  equation 


~      is  the  total  resistance  of 


PKIMAEY  BATTERIES  73 

the  entire  circuit,  and   (e)  is  the  electromotive  force  acting 
on  this  resistance. 

Fig.  35  shows  three  cells  connected  in  parallel  and  the 
battery  thus  formed  connected  to  a  resistance  (R). 

Fig.  36  shows  a  hydraulic  analogy  similar  to  the  con- 
nection of  cells  in  parallel.  The  pumps  (Pj)  and  (P2)  are 
so  connected  that  their  pressures  are  not  added,  but  the 
quantity  of  water  supplied  will  be  equal  to  that  supplied 
by  both  pumps. 

Example.  —  Six  cells  having  an  e.m.f.  of  1.5  volts  each  and 
an  internal  resistance  of  .6  ohm  each  are  connected  in 
parallel,  and  the  combination  is  then  connected  to  a  resist- 
ance of  10  ohms.  What  current  exists  in  the  resistance  when 
the  circuit  is  closed? 

Solution.  —  By  a  direct  substitution  in  equation  (71)  we 
have 

1.5  1.5 

I  =  -  =  --  =  0.148+ 

.6        10.1 
10  +  — 
6. 

Ans.    0.148+  ampere. 

82.  Series  and  Parallel  Combinations.—  A  very  common 
grouping  of  cells  is  a  combination  of  the  series  and  the  par- 
allel groups.  Suppose  there  are  (P)  groups  of  cells  and  each 
group  consists  of  (S)  cells  in  series.  The  total  number  of 
cells  is  then  equal  to  (SP).  The  e.m.f.  will  be  (Se)  volts, 
the  internal  resistance  of  each  set  will  be  (Sr)  ohms,  and 
the  internal  resistance  of  the  (P)  sets  combined  will  be 


ohms.     If  the  external  resistance  is   (R)   ohms,  then 

the  total  resistance  will  be     (R^^p)     ohms,  and  the  current 
produced  by  the  combination  will  be 

Se  PSe 

(72) 
PR  +  Sr 


74  PRACTICAL  APPLIED  ELECTRICITY 

Fig.  37  shows  a  battery  composed  of  three  groups  of  cells 
and  there  are  three  cells  connected  in  series  in  each  group. 
The  battery  is  connected  to  a  resistance  (R). 

Example. — A  battery  is  composed  of  nine  cells  connected, 
as  shown  in  Fig.  37,  to  an  external  resistance  of  10  ohms. 
The  e.m.f.  of  each  cell  is  1.5  volts;  each  cell  has  an  internal 
resistance  of  .5  ohm.  What  current  will  the  battery  supply 
when  the  circuit  is  closed? 

Solution. — Substituting  directly  in  equation   (72),  we  have 

3  X  3  X  1.5  13.5 

1  =  —  -  =  0.428  + 

(3  X  10)  +  (3  X  .5)        31.5 

Ans.     0.428+  ampere. 
83.     Advantage  of  Series  and  Par- 

^_  I        |        I  allel    Connections. — -Cells    are    con- 

'  |  r~|  r~|  I  ^  nected  in  parallel  when  it  is  desired 
to  obtain  a  large  current  through 
a  low  external  resistance.  When  the 
cells  are  so  grouped  they  are  equiva- 
lent to  one  large  cell,  and  will  have 
a  very  low  internal  resistance,  and 
when  connected  to  a  low  external 
resistance,  as  compared  to  the  inter- 
Fig.  37  nal  resistance,  the  current  will  be 
large.  If  the  external  resistance 

is  large,  the  current  will  be  small,  as  the  electromotive 
force  acting  is  small.  The  series  connection  is  employed 
when  the  external  resistance  is  the  principal  resistance  to 
overcome  and  the  maximum  current  strength  is  desired  in 
the  circuit. 

PROBLEMS  ON  GROUPING  OF  CELLS 

(1)  How    many    cells    should    be    connected    in    series    to 
cause  a  current  of  1.5  amperes  in  an  external  resistance  of 
8  ohms.     The  e.m.f.  of  each  cell  is  1.5  volts,  and  its  internal 
resistance  is  .2  ohm. 

Ans.     10  cells. 

(2)  How   many    cells  must   be    connected    in    parallel    to 
cause  a  current  of  2  amperes  in  an  external  resistance  of  .6 


HHH 
-HHH 


PRIMARY  BATTERIES  75 

ohm.     The  e.m.f.   of  each  cell  is  1.5  volts  and  its   internal 
resistance  is   1.2  ohms. 

Ans.     8  cells. 

(3)  Ten  cells,  each  having  an  e.m.f.  of  2.2  volts  and  an 
internal  resistance  of  .07  ohm,  are  connected  in  series  to  a  cir- 
cuit whose  resistance  is  4.3  ohms.    What  current  exists  in  the 
circuit? 

Ans.     4.4  amperes. 

(4)  Twenty  storage  cells  are  connected  in  series-multiple, 
there  being  five  groups  in  parallel  and  four  cells  in  series 
in  each  group.     The  e.m.f.  of  each  cell  is  2.2  volts  and  its 
internal  resistance  is  .05  ohm.     What  current  will  the  com- 
bination produce  through  an  external  resistance  of  .4  ohm? 

Ans.     20  amperes. 

(5)  Five  cells  are  connected  in  series.     Each  cell  has  an 
e.m.f.  of  2  volts  and  an  internal  resistance  of  .2  ohm.    What 
is  the  terminal  voltage  of  the  battery  on  open  circuit  and 
also   when   it   is   connected   to   an   external   resistance   of   4 
ohms? 

Ans.     Open-circuit   voltage  =  10    volts. 
Closed-circuit   voltage  =  8   volts. 

Note. —  (There  will  be  a  drop  in  terminal  voltage  when  the 
circuit  is  closed  on  account  of  the  internal  resistance.) 

(6)  Twenty  cells,  each  having  an  e.m.f.  of  2  volts  and  an 
internal  resistance  of  .2  ohm,  are  to  be  connected  so  that 
they   will   give   the   maximum    current   through   an    external 
resistance  of  1  ohm.    What  combination  should  be  used? 
Ans.     Two  groups,  in  parallel,  each  group  having  ten  cells 

in  series. 

Note. — (The  maximum  current  is  obtained  from  any  com- 
bination of  cells  when  they  are  so  connected  that  their 
combined  internal  resistance  is  equal  to  the  external  resist- 
ance to  which  they  are  connected). 

Solution. — Let  (S)  equal  the  number  of  cells  in  series  in 
any  one  group  and  then  (n  -t-  S)  will  equal  the  number  of 
groups  in  parallel.  Then  in  order  that  the  maximum  cuir- 
rent  be  obtained  from  the  battery 


76  PBACTICAL  APPLIED  ELECTKICITY 

SXr 
must  equal  1.0 


(n-K.8) 

or 

S  X  .2       .282       2S2       S2 

20  20         200       100 



8 

S2  =  100 

S=    10 

(7)  How  many  cells,   each  having  an   e.m.f.   of  2.2   volts 
and  an  internal  resistance  of  .005  ohm,  must  be  connected 
in  series  in  order  that  the  terminal  voltage  may  be  at  least 
44  volts  when  the  current  through  tLe  battery  is  40  amperes? 

Ans.  22  cells. 

(8)  The   terminal   voltage   of   a   battery   drops   from    1.8 
volts  on  open  circuit  to   1.5  volts   when  there  is   a  current 
of   6    amperes   through   the   battery.     What   is   the   internal 
resistance  of  the  battery? 

Ans.    .5  ohm. 


CHAPTER  V 

MAGNETISM 

84.  The    Magnet. — The   name    magnet    was   given    by   the 
ancients  to  certain  black  stones,  found  in  various  parts  of 
the   world,   principally    at    Magnesia    in    Asia    Minor,    which 
possessed   the  property   of  attracting  to  them   small   pieces 
of  iron  or  steel.     This  magic  property,  as  they  deemed  it, 
made  the  magnet-stone  famous;   but  it  was  not  until  about 
the  twelfth  century  that  such  stones  were  discovered  to  have 
the  still  more  remarkable  property  of  pointing  approximately 
north  and  south  when  freely  suspended  by  a  thread.     This 
property  of  the  magnet-stone  led   to   its   use   in    navigation, 
and  from  that  time  the  magnet  received  the  name  of  "lode- 
stone,"  or  "leading  stone."    The  natural  magnet,  or  lodestone, 
is   an   ore   of   iron,   and   is    called   magnetite.     Its    chemical, 
composition  is  Fe3O4.    This  is  found  in  quite  large  quantities 
in  Sweden,  Spain,  and  Arkansas,  U.   S.  A.,  and  other  parts 
of  the  world,  but  not  always  in  the  magnetic  state. 

85.  Artificial   Magnets. — If  a  piece  of  iron,  or,  better  still, 
a  piece  of  hard  steel,  be  rubbed  with  a  lodestone,  it  will  be 
found  to  possess  the  properties  or  characteristic  of  the  mag- 
net, viz,  it  will  attract  light 

bits  of  iron;  it  will  point  ap- 
proximately north  and  south 
if  hung  up  by  a  thread; 
and  it  can  be  used  to  magne- 
tize another  piece  of  iron  Fig.  38 
or  steel.  Magnets  made  in 
this  manner  are  called  artificial  magnets. 

Strong  artificial  magnets  are  not  made  from  lodestone, 
as  its  magnetic  force  is  not  strong,  but  by  methods  as  de- 
scribed under  "Electromagnetism."  Figs.  38  and  39  show, 
respectively,  a  natural  and  an  artificial  magnet,  each  of  which 

77 


78 


PRACTICAL  APPLIED  ELECTRICITY 


has  been  dipped  into  iron  filings;  the  filings  are  attracted 
and  adhere  in  tufts  at  the  ends. 

86.  Poles  of  a  Magnet. — Certain  parts  of  a  magnet  possess 
the  property  of  attracting  iron  to  a  greater  extent  than  do 
other  parts.  These  parts  are  called  the  poles  of  the  magnet. 

The  poles  of  a  bar  magnet, 
for  example,  are  usually 
situated  at  or  near  the 
ends  of  the  bar,  as  shown 
in  Fig.  38. 

87.     Magnetic  Needle.—- 
The  magnetic  needle  con- 
Fig.  39  sists  of  a  light  needle  cut 

out    of    steel,    and    fitted 

with  a  cap  of  glass,  or  agate,  by  means  of  which  it  can  be 
supported  on  a  sharp  point,  so  as  to  turn  with  very  little 
friction.  This  needle  is  made  into  a  magnet  by  being  rubbed 
on  a  magnet;  and  when  placed  on  its  support  will  turn  into 
the  rorth-and-south  position,  or,  as  we  should  say,  will  set 
itself  in  the  "magnetic  meridian."  The  end  of  the  needle 
that  points  toward  the  north  geographical  pole  is  called  the 
North  Pole,  and  is  usually  marked  with  the  letter  N,  while 
the  other  end  is  the  South  Pole. 

By  the  term  polarity  is 
meant  the  nature  of  the 
magnetism  at  some  particu- 
lar point,  that  is,  whether  it 
is  north  or  south-seeking 
magnetism.  The  compass 
sold  by  opticians  consists  of 
such  a  needle  balanced 
above  a  card  marked  with 
the  "points  of  the  compass" 

and  the  whole  placed  in  a  suitable  containing  case.  A  com- 
mon form  of  the  magnetic  needle  is  shown  in  Fig.  40. 

88.  Magnetic  Attraction  and  Repulsion. — When  the  two 
poles  of  a  magnet  are  presented  in  turn  to  the  north-pointing 
pole  of  a  magnetic  needle,  it  will  be  observed  that  one  pole 
of  the  magnet  attracts  it,  while  the  other  repels  it.  If  the 
magnet  is  presented  to  the  south-pointing  pole  of  the  mag- 
netic needle,  it  will  be. repelled  by  one  pole  and  attracted 


MAGNETISM  79 

by  the  other.  The  same  pole  that  attracts  the  north-pointing 
end  of  the  magnetic  needle  repels  the  south-pointing  end. 
As  the  needle  and  the  magnet  attract  each  other  when  unlike 
poles  are  presented,  and  repel  each  other  when  like  poles 
are  presented,  it  follows  that  like  poles  always  repel  each 
other  and  unlike  poles  always  attract  each  other.  Fig.  41 
shows  the  results  of  presenting  two  like  poles  and  Fig.  42 
shows  the  result  of  presenting  two  unlike  poles. 


Fig.  41  Fig.  42 

Two  equal  and  like  poles  are  said  to  have  unit  strength 
when  there  is  a  force  of  repulsion  between  them  of  one 
dyne  when  placed  one  centimeter  apart  in  air. 

89.  Magnetizable    Metals. — The  principal   magnetic  metals 
used  in  practice  are  steel  and  iron.    There  are  other  metals, 
such  as  nickel,  cobalt,   chromium,  and   cerium,   that  are  at- 
tracted  by  a   magnet,   but   very   feebly.     Of  this   last   class 
cobalt  and  nickel  are  the  best,  but  very  inferior  to  iron  or 
steel.    All  other  substances,  such  as  wood,  lead,  gold,  copper, 
glass,   platinum,   etc.,   may   be   regarded   as   unmagnetizable, 
or    nonmagnetic    substances.      Magnetic    attraction    or   repul- 
sion will,  however,  take  place  through  these  substances. 

90.  Magnetic     Force.— The    force    with    which    a    magnet 
attracts  or  repels  another  magnet,  or  any  piece  of  iron  or 
steel,  is  termed  its  magnetic  force.     The  value  of  this  mag- 
netic force  is  not  the  same  for  all  distances,  the  value  being 
greater  when  the  magnet  is  nearer,  and  less  when  the  magnet 
is  further  off.     The  value  of  this  force  of  attraction  or  repul- 
sion decreases  inversely  as  the  square  of  the  distance  from 
the  pole  of  the  magnet.     The  force  is  mutual,  that  is,  the 


80 


PBACTICAL  APPLIED  ELECTRICITY 


iron  attracts  the  magnet  just  as  much  as  the  magnet  attracts 
the   iron. 

91.  Magnetic    Lines    of    Force. — The    magnetic    force    pro- 
duced by  a  magnet  emanates  in  all  directions  from  the  mag- 
net.     The    direction    of    the    magnetic    force    at    any    point 
near   a   magnet    can   be    determined   by   means    of   a    small 
compass  needle  suspended  at  the  point  in  such  a  way  that  it 
is  free  to  move  in  any  direction.     The  direction  at  any  other 
point   can   be   determined   by   changing   the   position    of   the 
needle  with  respect  to  the  magnet.     Starting  with  the  needle 
near  one  end  of  the  magnet,  it  may  be  carried  toward  the 
other  end  and  an  imaginary  line,  drawn  in  such  a  way  that 
its  direction  at  any  point  corresponds  to  the   direction   as- 
sumed by  the  needle  at  that  point,  corresponds  to  what  is 
termed  a  line  of  force,  or  it  is  the  path  taken  by  a  north 
magnetic  pole  in  moving  from  the  north  to  the  south  pole 
of  a  magnet.     These  lines  of  force  start  at  the  north   pole 
of  a  magnet  and  terminate  at  the  south  pole.     Fig.  43  shows 
such  a  line. 

92.  Magnetic    Field. — The    region    surrounding    a    magnet 
which  is  permeated  by  magnetic  lines  of  force  is  called  a 


Fig.  43 


Fig.  44 


magnetic  field  of  force,  or  a  magnetic  field.  The  lines  of 
force  forming  a  magnetic  field  emanate  from  the  N-pole 
of  a  magnet,  pass  through  the  medium  surrounding  the 
magnet,  re-enter  the  S-pole  and  complete  their  path  by 
passing  from  the  S-pole  to  the  N-Pole  inside  the  magnet 
itself.  The  magnetic  field  surrounding  a  bar  magnet  is 
shown  in  Fig.  44.  All  magnetic  lines  form  closed  circuits 
and  there  must  be  two  or  more  magnetic  poles  (always  even) 
associated  with  each  of  these  circuits  except  in  the  case  of  a 
ring  magnetized  by  a  current,  which  will  be  discussed  later. 


MAGNETISM 


81 


The  region  we  speak  of  as  a  magnetic  field  is  capable  of 
acting  upon  magnets,  magnetic  materials,  and  conductors 
carrying  a  current  of  electricity.  The  lines  of  force  forming 
any  magnetic  field  are  assumed  to  have  two  properties: 
First,  they  tend  to  contract  in  length;  second,  they  repel 
each  other.  The  attraction  and  repulsion  of  unlike  and  like 
poles  can  be  accounted  for  by  assuming  the  lines  to  possess 
the  above  properties. 

93.  Making  Magnetic  Fields.— A  graphical  representation 
of  a  magnetic  field  may  be  made  by  placing  a  piece  of  card- 
board over  the  magnet  or  magnets  whose  field  you  want  to 
produce,  and  sprinkle  iron  filings  on  the  paper,  tapping  it 
gently  at  the  same  time.  The  iron  filings  are  composed  of 
a  magnet  material  and  arrange  themselves  in  the  direction 
of  the  lines  of  force  or  magnetic  field,  and  as  a  result  produce 
a  graphical  representation  of  the  field.  This  representation 
of  the  field  can  be  made  permanent  by  using  a  piece  of  paper 
that  has  been  dipped  in  paraffine  instead  of  the  cardboard. 


N 


Fig.  45 


Fig.  46 


The  paraffine  can  be  heated  by  means  of  a  warm  soldering 
iron,  or  other  warm  non-magnetic  material,  which  permits 
the  filings  to  imbed  themselves  in  the  wax  and  they  will  be 
held  firmly  in  place  when  the  paraffine  has  cooled. 

The  magnetic  field  that  exists  between  unlike  poles  is 
shown  in  Fig.  45,  and  the  field  between  like  poles  is  shown 
in  Fig.  46. 

94.  Distortion  of  Magnetic  Field. — The  direction  of  a  mag- 
netic field  is  influenced  by  the  presence  of  magnetic  material 
or  magnets.  When  a  magnetic  material  is  placed  in  any 
magnetic  field  that  exists  in  air,  the  form  of  the  field  will  be 
changed  because  the  material  is  a  better  conductor  of  mag- 
netic lines  than  air  and  the  lines  of  force  crowd  into  the 
material.  There  will  be  a  greater  number  of  magnetic  lines 


82 


PRACTICAL  APPLIED  ELECTRICITY 


in  a  given  area  in  the  iron  than  there  is  in  a  corresponding 
area  in  the  air.  A  magnetic  field  that  has  been  distorted, 
due  to  the  presence  of  a  piece  of  iron,  is  shown  in  Fig.  47. 
All  materials  that  conduct  magnetic  lines  better  than  air 
are  called  paramagnetic,  and  those  that  do  not  conduct  as 
well  as  air  are  called  diamagnetic  substances. 


Fig.  47 


Fig.  48 


95.  Magnetic  Induction. — Magnetism  may  be  communicated 
to  a  piece  of  iron  without  actual  contact  with  the  magnet. 
If  a  short,   thin,   unmagnetized   bar   of   iron   be   placed   near 
some   filings,   and   a   magnet   brought   near   to   the   bar,   the 
presence  of  the  magnet  will  induce  magnetism  in  the  bar,  and 
it  will  now  attract  the  iron  filings,  Fig.   48.     The  piece  of 
iron  thus  magnetized  has  two  poles,  the  pole  nearest  to  the 
pole  of  the  inducing  magnet  being  of  the  opposite  kind,  while 
the  pole  at  the  farther  end  of  the  bar  is  of  the  same  kind  as 
the  inducing  pole.    Magnetism  can,  however,  only  be  induced 
in   those   bodies   that   are   composed    of   magnetic   materials. 
It  is  now  apparent  why  a  magnet  should  attract  a  piece  of 
iron  that  has  never  been  magnetized;    it  first  magnetizes  it 
by  induction  and   then  attracts  it;    as  the   nearest  end  will 
be    a   pole    of   opposite    polarity,    it   will   be   attracted    with 
a  force  exceeding  that  with  which  the  more  distant  end  is 
repelled. 

96.  Retention  of   Magnetization. — Not  all  of  the  magnetic 
substances   can  be  used   in   making  permanent  magnets,  as 
some  of  them  do  not  retain  their  magnetism  after  being  mag- 
netized.   The  lodestone,  steel,  and  nickel,  retain  permanently 
the  greater  part  of  the  magnetism  imparted  to  them.     Cast 
iron  and  many  impure  qualities  of  wrought  iron  also  retain 
magnetism   imperfectly.     Pure,    soft   iron   is,   however,    only 


MAGNETISM  83 

temporarily  magnetic.  The  above  statements  can  be  illus- 
trated by  the  following  experiment:  Take  several  pieces 
of  soft  iron,  or  a  few  soft  iron  nails,  and  place  one  of  them 
in  contact  with  the  pole  of  a  permanent  magnet,  allowing  it 
to  hang  downward  from  the  magnet,  as  shown  in  Fig.  49. 
The  piece  of  iron  or  nail  is  held  to  the  magnet  because  it 
has  become  a  temporary  magnet,  due  to  the  .process  of  mag- 
netic induction.  Another  piece  can  be  hung  to  the  first,  and 
another  to  the  second,  etc.,  until  a  chain  of  four  or  five 
pieces  is  formed.  If  now  the  steel  magnet  be  removed  from 
the  first  piece  of  iron,  or  nail,  all  the  remaining  pieces  drop 
off  and  are  no  longer  magnets.  A  similar  chain  formed  of 
steel  needles  will  act  in  the  same  way,  but  they  will  retain 
their  magnetism  permanently. 

It  is  harder  to  get  the  magnetism  into  steel  than  into 
iron,  and  it  is  harder  to  get  the  magnetism  out  of  steel  than 
out  of  iron,  because  steel  resists  magnetization  or  demagneti- 
zation to  a  greater  extent  than  soft  iron.  This  power  of  resist- 
ing magnetization  or  demagnetization  is  called  hysteresis. 

97.  Molecular  Theory  of  Magnetism. — There  are  quite  a 
number  of  experimental  facts  that  lead  to  the  conclusion  that 
magnetism  has  something  to  do  with  the  molecules  of  the 


Fig.  49  Fig.  50 

substance,  since  any  disturbance  of  the  molecules  causes  a 
change  in  the  degree  of  magnetization.  If  a  test  tube  full 
of  hard  steel  filings  be  magnetized,  it  will  behave  toward  a 
compass  needle  or  other  magnet  as  though  it  were  a  solid 
bar  magnet,  but  it  will  lose  practically  all  of  its  magnet- 
ism as  soon  as  the  fillings  are  rearranged  with  respect  to 
each  other  by  giving  the  tube  several  good  shakes.  A 
needle  that  has  been  magnetized  will  lose  its  magnetism 
when  heated.  A  magnet  may  be  broken  into  any  number  of 


84  PRACTICAL  APPLIED  ELECTRICITY 

different  pieces  and  there  will  appear  at  each  break  an  N- 
pole  and  an  S-pole,  as  shown  in  Fig.  50.  The  strength  of 
the  poles  of  any  magnet  will  be  greatly  reduced  by  ham- 
mering, twisting,  or  bending  it.  A  theory  often  used  to  explain 
certain  magnetic  phenomena  is  as  follows:  In  an  unmagne- 
tized  bar  it  is  assumed  that  the  molecules  are  each  a  tiny 

magnet,  and  that  these 
molecules  or  magnets  are 
arranged  in  no  definite  way, 


except  that  the  opposite 
poles  neutralize  each  other 
throughout  the  bar.  The 
theoretical  arrangement  of 

the  molecules  in  an  unmagnetized  bar  is  shown  in  Fig. 
51.  When  the  bar  is  brought  into  a  magnetic  field,  the  tiny 
magnets  are  turned,  due  to  the  action  of  the  outside  force, 
so  that  the  N-poles  tend  to  point  in  one  direction  and  their 
S-poles  in  the  other.  The  arrangement  of  the  molecules  after 
the  bar  has  been  magnetized  is  shown  in  Fig.  52.  The 
opposite  poles  neutralize  each  other  in  the  middle  of  the  bar 
but  there  will  be  an  N^pole  found  at  one  end  and  an  S-pole 
at  the  other. 

The   ease   with   which   any 

material  may  be  magnetized   

as   compared   to    some   other 

material    will    depend     upon 

what    might    be    termed    the 

molecular  friction  of  the  ma-  Fig-  52 

terial.  Thus,  the  molecules  in 

a  bar  of  steel  offer  a  greater  resistance  to  a  change  in  their 

position  than  do  the  molecules  in  cast  iron.    Steel,  as  a  result, 

is  harder  to  magnetize  than  cast  iron,  and  it  will  also  retain 

its  magnetism  after  once  magnetized  better  than  cast  iron  for 

the  same  reason. 

98.  Application  of  Permanent  Magnets. — Permanent  mag- 
nets are  made  to  assume  many  different  forms,  depending 
upon  the  particular  use  to  which  they  are  to  be  placed.  In 
the  majority  of  cases  the  bar  forming  the  magnet  is  bent 
into  such  a  form  that  both  poles  will  produce  an  effect 
instead  of  only  one  pole.  Thus,  instead  of  using  a  straight  bar 
magnet  in  picking  up  a  piece  of  iron,  as  shown  in  Fig.  53,  the 


MAGNETISM 


85 


bar  can  be  bent  into  a  U-shape  and  both  poles  presented  to 
the  piece  to  be  picked  up  as  shown  in  Fig.  54.  The  effect 
of  the  two  poles  in  the  second  case  will,  of  course,  be  greater 


Fig.   53 


Fig.   54 


than  the  single  pole  in  the  first.    A  magnet  such  as  that  shown 
in  Fig.  54  is  called  a  horseshoe  magnet. 

Permanent  magnets  are  used  for  numerous  different  pur- 
poses, such  as  in  telephone  receivers,  relays,  ringers,  measur- 
ing instruments,  etc. 


CHAPTER  VI 

ELECTRON!  AGNETISM 

99.  Magnet  Field  Around  a  Conductor  Carrying  a  Current. — 
In  1819,  Oersted  discovered  that  a  magnetic  needle  was  dis- 
turbed by  the  presence  of  a  conductor  carrying  a  current, 
and  that  the  needle  always  tended  to  set  itself  at  right  an- 
gles to  the  conductor.  If  a  magnetic  needle  be  placed  below 


Fig.  55 

a  wire,  as  shown  in  Fig.  55,  the  current  in  the  wire  being 
from  left  to  right,  as  indicated  by  the  arrow,  the  needle 
will  tend  to  move  in  the  direction  indicated  by  the  curved 
arrows.  If  the  current  in  the  conductor  be  reversed,  the 
direction  of  the  magnetic  needle  will  be  reversed.  It  is  thus 
seen  that  there  is  a  magnetic  field  set  up  about  a  conductor 
carrying  a  current  and  that  the  direction  of  this  magnetic 
field  will  depend  upon  the  direction  of  the  current  in  the 
conductor.  Magnetism  set  up  in  this  way  by  an  electric 
current  is  called  electromagnetism. 

100.  Direction  of  an  Electromagnetic  Field. — Remembering 
that  the  direction  of  a  magnet  field  may  be  determined 
by  placing  a  compass  needle  in  the  field  -and  determining 
the  direction  in  which  the  N-pole  of  the  needle  will  point — 
this  being  taken  as  the  positive  direction — you  can  determine 
the  direction  of  the  magnetic  field  surrounding  a  conductor, 
produced  by  a  current  in  the  conductor.  The  small  circle 

86 


ELECTBOMAGNETISM 


8? 


in  Fig.  56  represents  the  cross-section  of  a  conductor  that 
can  be  imagined  as  passing  through  the  paper.  The  direc- 
tion of  current  in  this  conductor  is  away  from  the  observer, 
and  this  fact  is  indicated  by  the  plus  sign  (  +  )  inside  the 
circle.  A  compass  needle  placed  below  this  conductor  will 
set  itself  in  such  a  position  that  the  N-pole  is  toward  the 
left  and  the  S-pole  is  toward  the  right.  If  the  compass  needle 
be  placed  above  the  conductor,  as  shown  in  Fig.  57,  the  N- 
pole  will  point  toward  the  right  and  the  S-pole  toward  the 


Fig.   5(5 


left.  When  the  current  is  reversed  in  direction,  that  is,  the 
flow  is  toward  the  observer — which  is  indicated  by  the  minus 
sign  ( — )  inside  of  the  circle — the  positions  assumed  by  the 
compass  needle  will  be  just  the  reverse  of  those  shown  in 
Figs.  56  and  57. 


Fig.   58 

If  a  conductor  is  passed  through  a  small  opening  in  the 
center  of  a  piece  of  cardboard  that  is  supported  in  a  hori- 
zontal position,  as  shown  in  Fig.  58,  and  a  current  is  passed 
through  the  conductor,  the  field  may  be  explored  by  means 
of  a  small  compass  needle.  When  the  current  in  the  con- 


88 


PBACTICAL  APPLIED  ELECTKICITY 


ductor  is  down  through  the  cardboard,  as  indicated  by  the 
arrow  (I)  in  the  figure,  the  needle  will  assume  a  position 
at  right  angles  to  the  conductor  (neglecting  the  effect  of 
the  earth's  magnetic  field)  and  the  N-pole  will  point,  when 
you  are  looking  down  upon  the  cardboard,  in  the  direction 
the  hands  of  a  clock  move.  The  dotted  line  drawn  on  the 
surface  of  the  cardboard  indicates  the  path  that  an  N-pole 

would  move  in,  in  passing 
around  the  conductor.  The 
arrow   on   the   dotted   line 
indicates  the   direction   in 
which     the     pole     would 
move.      If   the    current    in 
the     conductor     were     re- 
versed,   the    direction    of 
motion,  or  the  direction  of 
the  field,  would  be  reversed. 
Iron     filings     may     be 
sprinkled  on  the  cardboard 
and    they    will    form    con- 
Fig.  59  centric    circles    about    the 
conductor      which      corre- 
spond to  the  lines  of  magnetic  force  produced  by  the   cur- 
rent.   A  field  formed  in  this  way  is  shown  in  Fig.  59. 

101.  Rules  for  Determining  the  Direction  of  a  Field  About 
a  Conductor  Carrying  a  Current.— There  are  a  number  of 
different  ways  of  remembering  the  relation  between  the  di- 
rection of  a  magnetic  field  and  the  direction  of  the  cur- 
rent producing  it.  A  very  simple  rule  that  is  known  as 
the  "right-hand  rule"  is  as  follows:  Grasp  the  conductor 
carrying  the  current  with  the  right  hand,  the  thumb  being 
placed  along  the  wire  and  the  fingers  being  wrapped  around 
the  wire;  then  the  fingers  point  in  the  direction  of  the 
magnetic  field  produced  by  the  current  in  the  wire  when 
the  thumb  points  in  the  direction  in  which  the  current  passes 
through  the  wire. 

If  a  person  looks  along  a  conductor,  carrying  a  current, 
in  the  direction  of  the  current,  the  direction  of  the  magnetic 
field  surrounding  the  conductor  will  be  clockwise. 

Another  rule  known  as  the  "right-hand  screw  rule"  is  as 
follows:  Consider  a  right-handed  screw  which  is  being 


ELECTEOMAGNETISM 


89 


screwed  into  or  out  of  a  block,  as  shown  in  Fig.  60.  If 
an  electric  current  is  supposed  to  exist  through  the  screw 
in  the  direction  in  which  the  screw  moves  through  the  block, 
then  the  direction  of  the  magnetic  field  will  correspond  to 
the  direction  in  which  the  screw  turns. 

102.  Strength  of  Magnetic  Field.— The  strength  of  any 
magnetic  field  is  measured  in  terms  of  the  number  of  lines 
of  force  per  unit  area,  usually  one  square  centimeter  per- 
pendicular to  the  direction  of  the  field.  The  symbol  used 
to  indicate  field  strength  is  the  letter  (H).  The  properties 
of  the  magnetic  field  surrounding  a  conductor  carrying  a 
current  are  the  same  as  those  possessed  by  the  magnetic 
field  produced  by  a  permanent  magnet.  The  strength  of  a 


Fig.  60 


Fig.  61 


magnetic  field  at  a  certain  point,  due  to  a  current  in  a  con- 
ductor or  a  permanent  magnet,  will  depend  directly  upon 
the  strength  of  the  current  in  the  conductor,  or  the  strength 
of  the  permanent  magnet,  and  inversely  as  the  square  of  the 
average  distance  the  point  is  from  the  conductor  or  perma- 
nent magnet. 

103.  Solenoid. — A  little  consideration  will  show  that  if  a 
current  be  carried  below  a  compass  needle  in  one  direction, 
and  then  back  in  the  opposite  direction  above  the  needle 
by  bending  the  wire  around,  as  shown  in  Fig.  61,  the  forces 
exerted  on  the  needle,  due  to  the  current  in  the  upper  and 
lower  portions  of  the  wire,  will  be  in  the  same  direction. 
If  the  needle  is  the  same  distance  from  each  portion  of  the 
circuit  the  effect  of  the  two  parts  will  be  just  double  that 


90  PRACTICAL  APPLIED  ELECTRICITY 

produced  by  either  part  acting  alone.  Hence,  if  the  wire 
be  coiled  about  the  needle,  each  additional  turn  will  produce 
an  additional  force  tending  to  turn  the  needle  from  its  nor- 
mal position.  The  magnetic  effect  of  any  current  can  be 
greatly  increased  in  this  way. 

A  cross-section  through  a  single  turn  of  wire  is  shown  in 

Fig.    62.      The    current    is 
away  from  the  observer  in 

/'     /     /'       ,''"^x      \      \     '•          the  upper  part  of  the  con- 

,       ductor>     and     toward     the 
'''       observer  in  the  lower  part, 
as    indicated    by   the    (  +  ) 
and  ( — )  signs.    The  direc- 
*         tion  of  the  magnetic  field 
^         surrounding      the      upper 
'\     \     V  _",-''       '      )       \       cross-section  will  be  clock- 
wise,  as  indicated  by  the 

Fig-  C'J  arrows      on      the      curves 

drawn  about  it,  while  the 

direction  of  the  field  surrounding  the  lower  cross-section  will 
be  counter  clockwise,  as  indicated  by  the  arrows,  since  the 
current  is  in  the  opposite  direction  in  the  lower  cross-section 
of  the  conductor  to   what 
it   is    in    the    uppe~   cross- 
section.      It    will    be    seen          ,-•***'  '*"*-, 
that  the   magnet   field  be-      ./         .-''',-"-     .--.   ,--.  "j^N. 
tween    the    two    cross-sec-        "x 
tions     of     the     conductor       -^I:*w 
or   through    the    center   of      ^ 
the  turn  is  toward  the  left       ••''^r-'' 
and  it  is  the  resultant  of      /'    ( 
the   two    fields    about   the       >xv.    '--.."".. 
two      cross-sections.      The                                                  .,,---'' 
field   is   stronger   between                          Fis-  63 
the  two  cross-sections  than 

it  is  outside,  which  is  indicated  by  a  larger  number  of  lines 
of  force  per  unit  of  area,  as  shown  in  the  figure. 

Increasing  the  number  of  turns  forming  the  coil  will  in- 
crease the  strength  of  the  magnetic  field  inside  the  coil, 
since  the  lines  of  force  that  surround  each  turn  seem  to 
join  together  and  pass  around  the  entire  winding  instead 


ELECTEOMAGNETISM 


91 


N 


of  passing  around  the  respective  conductors.  A  cross-sec- 
tion through  a  coil  composed  of  several  turns  is  shown  in 
Fig.  63.  A  few  of  the  lines  encircle  the  different  conductors, 
but  the  greater  portion  pass  entirely  through  the  center  of 
the  coil  and  around  the  total  number  of  turns.  Such  coils 
are  called  solenoids. 

104.  Polarity  of  Solen- 
oids.— A  solenoid  carrying 
a  current  exhibits  all  the 
magnetic  effects  that  are 
shown  by  permanent  mag- 
nets. If  a  solenoid  that 
is  carrying  a  current  be 
suspended  so  that  it  is 
free  to  swing  about  a  ver- 
tical axis,  its  own  axis 
being  horizontal,  it  will 
move  into  an  approxi- 
mately north  and  south 
position,  exactly  like  a 
permanent  magnet.  A  so- 
lenoid supported  in  this 
way  is  shown  in  Fig.  64. 
They  attract  and  repel 
magnets,  pieces  of  iron,  Fig.  64 

and  other  solenoids.     See 
Fig.  65. 

The  polarity  of  any  solenoid  may  be  determined,  when 
the  direction  of  the  current  is  known,  by  a  simple  application 
of  any  one  of  the  rules  given  in  section  (101).  The  lines  of 
magnetic  force  inside  the  solenoid  pass  from  the  S-pole 
to  the  N-pole  and  outside  the  solenoid  from  the  N-pole  to 
the  S-pole.  Referring  to  Fig.  63,  you  see  that  the  end  of 
the  solenoid  toward  the  left  will  be  the  S-pole  and  the  end 
toward  the  right,  the  N-pole. 

A  simple  rule  by  which  the  polarity  of  a  solenoid  may  be 
determined,  if  the  direction  of  the  current  around  the  wind- 
ing is  known,  is  as  follows:  If  you  face  one  end  of  the 
solenoid  and  the  current  is  around  the  winding  in  a  clock- 
wise direction,  the  end  nearest  you  will  be  the  S-pole  and 
the  other  end  will  be  the  N-pole.  If  the  direction  of  the  cur- 


92  PRACTICAL  APPLIED  ELECTRICITY 

rent  around  the  winding  is  counter  clockwise,  the  end  near- 
est you  will  be  the  N-pole  and  the  other  end,  the  S-pole. 

Another  simple  rule  is  to  grasp  the  solenoid  with  the  right 
hand  with  the  fingers  pointing  around  the  coil  in  the  direc- 
tion of  the  current,  the  thumb  will  then  point  toward  the 
N-pole  of  the  coil,  as  shown  in  Fig.  66. 


Fig.  65 


Fig.  66 


105.  The  Toroid.— If  a  solenoid  is  bent  around  until   its 
two   ends   meet,   or  if   a   winding   is   placed   on   a   ring,   the 
arrangement  thus   produced   will   be   a  toroid.     By   winding 
the    various    turns    closely    and    uniformly    over    the    entire 
periphery   of   the   ring,   the   lines   of   force   produced    inside 
the  ring  by  a  current  in  the  winding  will  form  closed  curves 
whose  paths  are  entirely  with- 
in   the    turns    composing    the 

winding;  consequently,  there 
are  ro  external  magnet  poles. 
Such  a  coil  is  shown  in  Fig.  67. 

106.  Permeability.    —    The 
number  of  magnetic  lines  pro- 
duced inside   a   solenoid,   with 
an  air  core,  can  be  greatly  in- 
creased by  introducing  a  piece 
of  iron,  even  though   the  cur- 
rent in  the  winding  of  the  so- 
lenoid remains  constant.     This 

is  due  to  the  fact  that  the  iron  is  a  better  conductor 
of  magnetic  lines  than  air.  The  relation  between  the  num- 
ber of  lines  of  force  per  unit  area  inside  the  solenoid  after 
the  iron  has  been  introduced,  designated  by  (/3),  to  the 


Fig.   6' 


ELECTKOMAGNETISM 


93 


number  of  lines  per  unit  of  area  for  an  air  core,  which  is 
the  field  strength,  designated  by  (#),  is  called  the  permea- 
bility, designated  by  (/*). 

fi 
M  =  —  (73) 

H 

The  permeability  of  a  given  sample  of  iron  is  not  constant 
because  the  value  of  (/3)  does  not  increase  at  the  same 
rate  (H)  increases.  Curves  showing  the  relation  between 
the  two  quantities  for  wronght  iron,  cast  iron,  and  cast  steel 


ZO     30     40     SO      60      70      80     90  .  100    110     IZO     150    140    150    160 

Fig.  68 

are  shown  in  Fig.  68.  The  permeability  of  these  different 
kinds  of  iron  can  be  determined  for  any  value  of  (0)  or 
(H)  by  dividing  the  value  of  (/3)  for  any  point  on  the 
curve  by  the  corresponding  value  of  (fl). 

The  sharp  bend  in  the  curve  is  called  the  "knee"  of  the 
curve.  The  iron  is  very  nearly  saturated  at  this  point  be- 
cause any  further  increase  in  (H)  produces  a  small  increase 
in  (j8)  as  compared  to  what  a  corresponding  increase  in 
(H)  would  do  below  the  knee  of  the  curve. 

107.  Magnetomotive  Force.  —  The  magnetomotive  force 
(abbreviated  m.m.f.)  of  a  coil  carrying  a  current  is  its  total 
magnetizing  power.  When  a  current  passes  around  a  core 
several  times,  as  shown  in  Fig.  69,  the  magnetizing  power 


94  PRACTICAL  APPLIED  ELECTRICITY 

is  proportional  both  to  the  strength  of  the  current  and  the 
number  of  turns  in  the  coil.  The  product  of  the  current  in 
the  coil  and  the  number  of  turns  composing  the  coil  is 
called  the  ampere-turns.  The  magnetizing  power  of  the 
current  is  independent  of  the  size  of  the  wire,  the  area  of 

the  coils,  or  their  shape,  and  re- 
mains the  same  whether  the 
turns  are  close  together  or  far 
apart.  It  has  been  found  by 
experiment  that  one  ampere 
Fig.  69  turn  sets  up  1.2566  units  of  mag- 

netic   pressure.     Hence,    if    (n) 

represents  the  number  of  turns  in  the  coil  and  (I)  represents 
the  current  in  amperes  through  each  turn,  the  magnetomotive 
force  is 

m.m.f.  =  1.2566  X  n  X  I  (74) 

The  gilbert  is  the  unit  in  which  magnetomotive  force  is 
measured.  One  gilbert  is  equal  to  (1  -=-  1.2566)  ampere-turn. 
Magnetomotive  force  or  magnetic  pressure  corresponds  to 
electromotive  force  and  electrical  pressure  in  the  electrical 
circuit. 

The  m.m.f.  acting  in  any  magnetic  circuit  encounters  a 
certain  opposition  to  the  production  of  a  magnetic  field, 
just  as  an  electrical  pressure  encounters  a  certain  opposi- 
tion in  the  electrical  circuit  to  the  production  of  a  current. 
The  opposition  in  the  magnetic  circuit  is  called  the  reluc- 
tance, represented  by  (E),  of  the  circuit  and  its  value  will 
depend  upon  the  materials  composing  the  circuit  and  the 
dimensions  of  the  circuit. 

The  total  number  of  magnetic  lines  of  force,  called  the 
magnetic  flux,  represented  by  ($),  produced  in  any  magnetic 
circuit  will  depend  upon  the  m.m.f.  acting  on  the  circuit 
and  the  total  reluctance  of  the  circuit,  just  as  the  current 
in  an  electrical  circuit  depends  upon  the  electrical  pressure 
acting  upon  the  resistance  of  the  circuit.  The  unit  of  mag- 
netic flux  is  the  maxwell,  and  it  is  equal  to  one  line  of  force. 
The  gauss  is  the  unit  of  flux  density,  and  it  is  equal  to  one 
line  of  force  per  unit  of  area. 

Magnetomotive  force 

Number  of  lines  = (75) 

Reluctance 


ELECTKOMAGNETISM  95 


(76) 


108.  Reluctance.  —  The  reluctance  of  any  magnetic  cir- 
cuit depends  upon  the  dimensions  of  the  circuit  and  the 
kind  of  material  composing  the  circuit.  It  varies  directly 
as  the  length  of  the  circuit  and  inversely  as  the  area,  all 
other  conditions  remaining  constant.  The  reluctance  of  any 
given  volume  varies  inversely  as  the  permeability  of  the 
material  filling  the  volume. 

Length  in  centimeters 
Reluctance  = 

Permeability  X  cross-section  in  sq.  cm. 

I 
E  =  (77) 


The  unit  in  which  reluctance  is  measured  is  called  the 
oersted  and  it  is  equal  to  the  reluctance  of  a  cubic  centi- 
meter of  air. 

Reluctances  can  be  added  in  the  same  way  as  resistances. 
If  a  magnetic  circuit,  such  as  that  of  the  dynamo,  is  com- 
posed of  a  number  of  different  kinds  of  materials,  such  as 
cast  iron,  wrought  iron,  air,  etc.,  calculate  the  reluctance 
of  each  part  by  the  above  equation,  and  add  these  reluc- 
tances together  to  give  the  total  reluctance  of  the  entire 
magnetic  circuit.  The  value  of  the  permeability  to  use  in 
the  above  equation  will,  of  course,  depend  upon  the  number 
of  magnetic  lines  the  various  parts  of  the  circuit  are  to 
conduct  per  unit  of  area.  The  permeability  of  air  is  always 
unity. 

Example.  —  An  iron  ring  has  a  rectangular  cross-section  of 
four  square  centimeters  and  a  mean  length  of  20.5  centi- 
meters. A  slot  is  cut  in  this  ring  .5  centimeters  wide  and 
the  ring  is  wound  with  1000  turns  of  wire.  What  current 
must  there  be  in  the  winding  in  order  that  there  will  be 
100000  magnetic  lines  produced  in  the  air  gap?  Take  the 
permeability  of  the  iron  equal  to  1000. 

Solution.  —  The  reluctance  of  the  iron  portion  of  the  cir- 
cuit can  be  determined  by  substituting  in  equation  (77)  : 


PBACTICAL  APPLIED  ELECTKICITY 


20  1 

E  = =  • oersted 

1000  X  4        200 
The  reluctance  of  the  air  gap  will  be 

'.5 

E  =  =  ys  oersted 

1X4 

Total  reluctance  is 

11  13 

1 = =  .13  oersted 

8         200         ICO 

Substituting   the   values   of    (E),    (n),   and    ($)    in  equations 
(74)  and  (76)  gives 

L2566  X  1000  X  I 

100  000  = 

.13 

1.2566  X  1000  X  I  =  13  000 
1256.61  =  13000 
1  =  10.34 


Ans.     10.34  amperes. 


Example. — The  magnetic 
circuit,  shown  in  Fig.  70, 
is  rectangular  in  cross-sec- 
tion, the  dimensions  per- 
pendicular to  the  paper  be- 
ing 3  centimeters.  The 
permeability  of  the  iron  is 
1000.  The  armature  (A) 
is  .5  centimeter  from  eacii 
magnet  core.  There  are 
500  turns  in  each  coil  and 
each  turn  is  carrying  a 
current  of  10  amperes. 
What  is  the  value  of  the 
total  number  of  magnetic 
lines  produced  in  the  air 
gaps? 


Fig.   70 


Solution.— The  total  length  of  path  in  air  is 
2  x  .5  =  1    cm. 


ELECTROMAGNETISM  97 

The  area   of  the   magnetic   circuit   is   the   same   throughout 
and  is  equal  tc 

2  X  3  =  6  sq.  cm. 

The  reluctance  of  the  air  gaps  is  equal  to 

I  1  1 

E  = = =  — 

A*  A  1X6        6 

The  length  of  the  magnetic  circuit  in  the  iron  is 

TT  X  d 

(2  X  5)  +  (2  X  10)  +  4  (—     — )  =  33.1416  cm. 
4 

(Note — The  circuit  is  taken  as  a  curve  about  the  corners.) 
The  reluctance  of  the  iron  portion  of  the  magnetic  circuit 
will  be 

33.1416 

E  = =  .005  523  6  oersted 

1000  X  6 

The  total  reluctance  will  be 

h  .0055236  =  .17219  oersted 

6 

Substituting  the  values  of  (I),  (n),  and  (E)  in  equation  (76) 
gives 

1.2566  X  2  X  500  X  10 

*  = =72970. 

.17219 
Ans.     72970.  maxwells  (approx.). 


PROBLEMS  ON    MAGNETISM 

(1)  A  magnetic  circuit  is  40  cm.  in  length,  has  a  cross- 
section  of  4  square  centimeters,  and  is  composed  of  a  material 
whose  permeability  is  1500.  What  is  the  reluctance  of  the 
circuit? 

1 

Ans.    oersted. 

150 


98  PEACTICAL  APPLIED  ELECTRICITY 

2.     What  is  the  m.m.f.  in  gilberts  produced  by  a  current 
'   7.5   amperes   thr 
cuit  of  1200  turns? 


of   7.5   amperes   through   a   winding   around   a   magnetic   cir- 


Ans.     11  309. +  gilberts. 

(3)  A  magnetic  circuit   is  composed  of  three  parts   con- 
nected  in    series,   having  reluctances   of   .032,   .015,   and   .053 
oersted,   respectively.       What   m.m.f.   would   be   required   to 
produce  a  flux  of  10  000  maxwells? 

Ans.     1000  gilberts. 

(4)  How  many  turns  would  be  required  in  a  coil  to  pro- 
duce the  above  m.m.f.,  if  each  turn  is  to  carry  a  current  of 
1  ampere? 

Ans.     795  turns   (approx.). 

(5)  It  is  desired  to  magnetize  a  piece  of  iron  until  there 
are  6000  lines  per  square  centimeter.     What  cross-section  is 
required  to  have  a  total  of  100000  lines? 

Ans.     16%  sq.  cm. 

(6)  Two  magnetic  circuits  are  acting  in  parallel  and  they 
have  reluctances  of  .05  and  .04  oersted  respectively.    What 
is   the  total   reluctance   of  the   two   combined? 

Ans.     .0222  oersted. 

(Note:      Add   reluctances   in   parallel   the   same   as   resist- 
ances.) 

109.  Electromagnet. — A   simple   electromagnet  consists   of 
a   piece   of   iron   about   which    is    wound    an    electrical    con- 
ductor through  which  a  current  of  electricity  may  be  passed. 
Commercial  electromagnets  assume  numerous  different  forms 
depending  upon  the  particular  use  to  which  they  are  to  be 
placed.     They  are  used  in  electric  bells,  telephones,  relays, 
circuit    breakers,    generators,    motors,    lifting    magnets,    etc. 
The  use  of  the  electromagnet  in  handling  magnetic  materials 
has  become  quite  common  in  recent  years.     A  magnet  manu- 
factured   by   the    Electric    Controller    and    Supply    Company, 
Cleveland,  Ohio,  which  is  used  for  the  above  purpose,  is  shown 
in  Fig.  71. 

110.  Hysteresis. — If  a   piece   of  iron  be   magnetized,  then 


ELECTEOMAGNETISM 


99 


demagnetized  and  magnetized  in  the  opposite  direction  and 
again  demagnetized  it  will  be  found  that  the  degree  of 
magnetization  will  be  different  for  the  same  value  of  (H) 
depending  upon  whether  the  field  is  increasing  or  decreasing 
in  strength.  The  magnetization  of  the  iron  lags  behind  the 
magnetizing  force  and,  as  a  result,  the  values  of  (/3)  for 


Fig.  71 


certain  values  of  (H)  will  be  greater  when  the  magnetizing 
force  is  decreasing  than  they  will  be  for  the  same  values  of 
(H)  when  the  magnetizing  force  is  increasing.  Fig.  72 
shows  the  relation  between  (/3)  and  (H)  when  the  iron 
is  carried  through  what  is  termed  a  complete  cycle;  that  is, 
it  is  magnetized  to  a  maximum  positive  (/3),  as  at  (a)  in 
the  figure;  then  demagnetized  and  magnetized  to  a  maximum 
negative  (/3),  as  at  (b)  in  the  figure,  which  gives  the  upper 
curve  (acb).  The  lower  curve  (b  d  a)  is  obtained  in  a 
similar  way  by  demagnetizing  the  sample  from  a  negative 
(/3)  to  zero  and  then  magnetizing  it  to  a  maximum  posi- 
tive (|3),  returning  the  iron  to  its  original  magnetic  condition, 
which  completes  the  cycle. 

111.     Hysteresis    Loss. — When    a   piece    of   iron    is    carried 
through  a  magnetic  cycle,  as  described  in  the  previous  sec- 


100 


PRACTICAL  APPLIED  ELECTRICITY 


tion,  all  the  energy  spent  in  magnetizing  it  is  not  returned  to 

the  circuit  when  the  iron  is  demagnetized,  which  results  in 

a  certain  amount  of  electrical 
energy  being  expended  to 
carry  the  iron  through  the 
cycle.  This  energy  appears 
in  the  iron  as  heat.  The  en- 
ergy lost  per  cycle  depends 
upon  the  kind  of  iron  being 
tested,  the  volume  of  the 
sample,  and  the  maximum 
value  of  (]8)  raised  to  the  1.6 
power. 

Joules  (energy  per  cycle)  = 
V  X  jSi.e  X  -n  X  10-7         (78) 
The   constant   (77)   takes  into 
account  the  kind  of  iron  being 
Fig   72  tested  and  (V)  is  the  volume 

in  cubic  centimeters.     If  the 

iron  is  carried  through  (f)  cycles  per  second,  the  loss  of  power 

in  watts  is  given  by  the  equation 

Wh  =  77XfXVX  ,3i.c  x  10-7   watts  (79) 


TABLE  NO.  VI 

VALUE   OF   HYSTERETIC   CONSTANT    (77)     FOR    DIFFERENT 
MATERIALS 

Best  annealed  transformer  sheet  metal.  .  .........  001 

Thin  sheet  iron  (good)  .................  .........  003 

Ordinary  sheet  iron  .............................  004 

Soft  annealed  cast  steel  .........................  008 

Cast  steel  .....  .................................  012 

Cast  iron  .......................................  016 

Example.  —  A  piece  of  iron  is  magnetized  to  a  maximum  (0) 
of  9000  lines  per  sq.  cm.  It  is  carried  through  60  complete 
cycles  per  second.  What  is  the  power  lost  in  10  cubic  centi- 
meters if  the  hysteretic  constant  (77)  is  .003? 

Solution.  —  In  order  to  raise  the  value  of  (/3)  to  the  1.6 
power  you  must  make  use  of  logarithms.  (A  description  of 
the  use  of  logarithms  is  given  in  Chapter  20.)  In  the  table 
of  logarithms  you  will  find  opposite  the  number  900  the 
mantissa  95424.  (The  mantissa  of  the  logarithm  of  900  is 


ELECTROMAGNETISM  101 

the  same  as  the  mantissa  of  the  logarithm  of  9000.) 
Place  the  figure  3,  the  characteristic,  before  this  num- 
ber, which  is  one  less  than  the  number  of  significant  figures 
in  9000  and  you  have  the  log  9000  =  3.95424.  Multiply 
this  log  by  1.6  and  you  have  6.326  784.  Now  6.326  78  is  the 
log  of  the  result  you  want  to  obtain.  Looking  up  the  man- 
tissa 32678  in  the  table,  you  find  it  corresponds  to  2122. 
The  result  must  contain  seven  figures  before  the  decimal 
point  (because  the  characteristic  is  six),  hence,  the  result 
is  2.122  X  106.  Substituting  this  value  in  equation  (79), 
together  with  the  values  of  (f),  (V),  and  (77),  gives 

Wh  =  .003  X  60  X  10  X  2.122  X  106  X  10-7 

=  .18  X.  2.122  =  .38 

Ans.     .38  watts. 

112.  Law  of  Traction.—  The  formula  for  the  pull  of,  or  lift- 
ing power  of,  an  electromagnet  when  it  is  in  actual  contact 
with  the  object  to  be  lifted  is 

/32A 
Pull  in  pounds  =  -  (80) 

72  134  000 

In  the  above  equation  (/3)  is  the  number  of  lines  per  square 
inch  and  (A)  is  the  area  of  contact  in  square  inches.  The 
value  of  (/3)  required  to  produce  a  given  pull,  when  the  area 
of  contact  is  known,  can  be  calculated  by  the  use  of  the 
equation 

Pull  in  pounds 

-  (81) 


Area  in  square  inches 
In  the  above  equation  (/3)  will  be  lines  per  square  inch. 


CHAPTEE  VII 

ELECTROMAGNETIC  INDUCTION— FUNDAMENTAL 
THEORY   OF  THE    DYNAMO 

113.  Electromagnetic  Induction. — In  1831,  Michael  Faraday 
discovered  that  an  electrical  pressure  was  induced  in  a  con- 
ductor that  was  moved  in  a  magnetic  field,  when  the  direction 
of  motion  of  the  conductor  was  such  that  it  cut  across  the 
lines  of  force  of  the  field.     If  this  conductor  forms  part  of  a 
closed  electrical  circuit,  the  electromotive  force  induced  in  it 
will  produce  a  current.     Currents  that  are  produced  in  this 
way   are   called   induction   currents   and   the   phenomenon   is 
termed   electromagnetic   induction.     In   this   great   discovery 
lies  the  principle  of  the  operation  of  many  forms  of  commer- 
cial electrical   apparatus,  such  as  dynamos,   induction   coils, 
transformers,  etc. 

114.  Currents  Induced  in  a  Conductor  by  a  Magnet. — If  a 
conductor   (AB),  Fig.  73,  that  is  connected  in  series  with  a 
galvanometer  (G),  located  so  that  it  is  not  influenced  to  any 
great   extent   by   the   permanent   magnet,   be    moved    in   the 
field  of  the  magnet,  the  moving  system  of  the  galvanometer 
will  be  deflected  to   the    right   or   left  of  the  zero   position. 
This  deflection  is  due  to  a  current  in  the  circuit  which  is 
caused    by    the    induced    e.m.f.    in    the    conductor    that    was 
moved  in  the  magnetic   field.     When   the  movement  of  the 
conductor  in  the  field  ceases,  the  galvanometer  system  will 
return  to  its  zero  position,  which  indicates  there  is  no  cur- 
rent and  hence  no  induced  e.m.f.  in  the  circuit.     Hence,  the 
conductor  must  be  actually  cutting  the  magnet  lines  of  force 
in  order  that   there   be   an   induced   e.m.f.   produced   in   the 
circuit.     If  the  conductor   was  moved  downward  across  the 
field  in  the  above  case  and  the  deflection  of  the  galvanom- 
eter needle  was  to  the  right,  it  will  be  found,  upon  moving 
the  conductor  upward  across  the  field  or  in  the  opposite  direc- 

102 


ELECTEOMAGNETIC  INDUCTION 


103 


tion  to  its  motion  in  the  first  case,  that  the  galvanometer 
needle  will  be  deflected  to  the  other  side  of  its  zero  posi- 
tion.    Since  the  direction  in  which  the  needle  of  the  galva- 
nometer is  deflected  depends  upon  the  direction  of  the  current 
through  its  winding,  it  is  apparent  the  current  in  the  circuit 
in   the   second   case   is   in 
the    opposite    direction    to 
what    it    was   in   the   first 
case;  and  since  the  current 
is     due     to     the     induced 
e.m.f.     in     the     conductor 
(AB),   it  must  also  be  in 
the  opposite  direction.    If 
the  motion  of  the  conduc- 
tor in  the  magnetic  field  is 
continuous,   up   and   down 
past  the  end  of  the  mag- 
net, there  will  be  a  current  FJg-  73 
through  the  galvanometer 

first  in  one  direction  and  then  in  the  opposite  direction,  and 
the  galvanometer  needle  will  swing  to  the  right  and  left  of 
its  zero  position.  The  motion  of  the  conductor,  however, 
may  be  rapid  enough  so  that  the  galvanometer  needle  has 
not  sufficient  time  to  take  its  proper  position  with  respect 
to  the  current  in  the  conductor  and  as  a  result  it  remains 
practically  at  zero,  the  vibration  or  deflection  to  the  right 
or  to  the  left  being  very  small. 

The  same  results  can  be  obtained  by  using  the  opposite 
pole  of  the  magnet,  except  the  deflection  of  the  galvanometer 
needle  due  to  a  given  direction  of  motion  of  the  conductor 
will  be  just  the  reverse  of  what  it  was  with  the  other  pole. 
This  shows  that  there  is  some  definite  relation  between  the 
direction  of  motion  of  the  conductor,  the  direction  of  the  mag- 
netic field,  and  the  direction  in  which  the  induced  e.m.f.  acts. 
If  the  wire  were  held  stationary  and  the  magnet  moved,  the 
same  results  would  be  obtained  as  though  the  wire  were 
moved  past  the  magnet.  Hence,  it  is  only  necessary  that 
there  be  a  relative  movement  of  the  conductor  and  the 
field;  either  may  remain  stationary.  An  electromagnet  may 
be  used  instead  of  the  permanent  magnet  and  the  same 
results  will  be  obtained  under  similar  conditions. 


104  PRACTICAL  APPLIED  ELECTKICITY 

If  the  conductor  were  moved  very  slowly  across  the  mag- 
netic field,  the  galvanometer  needle  would  be  deflected 
through  a  much  smaller  angle  than  it  would  be  if  the  con- 
ductor were  moved  faster  across  the  field.  The  deflection 
of  the  galvanometer  needle  depends  upon  the  value  of  the 
current  through  its  winding  and  since  the  deflection  is 
smaller  when  the  conductor  is  moved  slowly  than  it  is  when 
the  conductor  is  moved  fast,  it  must  follow  that  the  induced 
e.m.f.  for  a  slow  movement  of  the  conductor  is  less  than  it 
is  for  a  fast  movement,  even  though  all  the  magnetic 
lines  of  force  forming  the  magnetic  field  be  cut  by.  the  con- 
ductor. The  above  results  show  that  the  value  of  the 
e.m.f.  induced  in  a  conductor,  due  to  the  relative  motion  of 
the  conductor  and  a  magnetic  field,  depend  upon  the  rate 
at  which  the  conductor  is  moving.  If  a  second  conductor 
be  connected  in  series  with  the  first,  so  that  their  induced 
e.m.f.'s  act  in  the  same  direction,  the  resultant  e.m.f.  is 
increased.  This  is  equivalent  to  increasing  the  effective 
length  of  the  conductor  in  the  magnetic  field. 

The  induced  e.m.f.  may  be  increased  by  placing  a  second 
magnet  along  the  side  of  the  first  so  that  their  like  poles 
are  pointing  in  the  same  direction.  This  second  magnet  in- 
creases the  strength  of  the  magnetic  field  and  the  conductor 
cuts  more  lines  of  force  due  to  any  movement. 

If  the  conductor  be  moved  in  a  path  parallel  to  the  lines  of 
force  forming  the  magnetic  field  or  along  its  own  axis,  there 
will  be  no  deflection  of  the  galvanometer  needle,  which  indi- 
cates there  is  no  current  in  the  circuit  and  hence,  no  in- 
duced e.m.f.  Then,  in  order  that  there  be  an  induced  e.m.f. 
set  up  in  a  conductor  due  to  Us  movement  with  respect  to  a 
magnetic  field,  the  path  in  which  the  conductor  moves  must 
make  some  angle  with  the  direction  of  the  magnetic  lines  of 
force.  The  value  of  the  induced  e.m.f.  due  to  the  movement 
of  a  conductor  in  a  magnetic  field  will  increase  as  the  angle 
between  the  direction  of  the  lines  of  force  and  the  path 
in  which  the  conductor  moves  increases,  and  it  will  be  a 
maximum  when  the  conductor  moves  in  a  path  perpendicular 
to  the  direction  of  the  magnetic  field  and  perpendicular  to 
itself. 

There  will  be  an  induced  e.m.f.  set  up  in  the  conductor 
even  though  the  circuit  of  which  the  conductor,  forms  a  part 


ELECTED  MAGNETIC  INDUCTION  105 

be  open.  This  induced  e.m.f.  will  exist  between  the  ter- 
minals of  the  circuit  where  it  is  opened,  just  the  same  as  an 
e.m.f.  exists  between  the  terminals  of  a  battery  that  is  on 
open  circuit. 

The  question  naturally  arises:  Is  the  magnet  weakened 
when  it  is  used  in  producing  induced  currents  in  a  conductor 
as  previously  described,  and  if  not,  what  is  the  source  of 
energy  that  causes  the  current  to  exist  in  the  conductor? 
The  magnet  is  in  no  way  weakened  when  it  is  used  as  pre- 
viously described,  and  the  induced  current  is  produced  by 
the  expenditure  of  muscular  energy  just  as  an  expenditure 
of  chemical  energy  in  a  cell  produces  an  electrical  current 
in  a  closed  circuit  to  which  the  cell  is  connected.  When 
a  conductor  with  a  current  in  it  is  located  in  a  magnetic 
field  in  a  position  other  than  parallel  to  the  field,  there  is 
a  force  produced  which  tends  to  cause  the  conductor  to  move 
across  the  field.  The  direction  of  this  force  is  just  oppo- 
site to  the  one  that  must  be  applied  to  the  conductor  to 
cause  it  to  move  so  there  will  be  an  induced  e.m.f.  set  up 
which  will  produce  the  current.  In  other  words,  the  induced 
e.m.f.  set  up  in  a  conductor  will  always  be  in  such  a  direc- 
tion that  the  current  produced  by  it  will  oppose  the  motion 
of  the  conductor. 

115.  Currents  induced  in  a  Coil 
by  a  Magnet. — If  a  coil  of  wire  (C) 
be  connected  in  series  with  a  gal- 
vanometer (G),  as  shown  in  Fig.  ?A«il— JM 
74,  a  deflection  of  the  galvanom- 
eter needle  can  be  produced  by 
thrusting  a  magnet  (M)  in  and  out 

j  of    the    coil.      When    the    magnet   is 
thrust  into  the  coil,  a  deflection  of 

•  the  needle  will  be  produced,  say,  to 
the  right,  and  when  the  magnet  is 

withdrawn  a  deflection  of  the  needle  will  be  produced  to  the 
left.  If  the  magnet  be  turned  end  for  end,  the  deflections  of 
the  galvanometer  needle  will  be  just  the  reverse  of  what 

'they  were  for  the  previous  arrangement.  If  the  coil  (C)  be 
turned  through  an  angle  of  180  degrees — so  that  the  side  that 
was  originally  toward  the  magnet  will  now  be  away  from  it— 
and  the  magnet  be  placed  in  its  original  position,  the  deflec- 


106  PEACT1CAL  APPLIED  ELECTKICITY 

tions  of  the  galvanometer  needle  produced  by  a  movement 
of  the  magnet  in  or  out  of  the  coil  will  correspond  in  direc- 
tion to  those  produced  when  the  coil  was  in  its  original 
position  and  the  magnet  had  been  turned  end  for  end. 

If  the  coil  be  moved  on  or  off  of  the  magnet,  the  same  effect 
is  produced  as  would  be  produced  by  moving  the  magnet  in  or 
out  of  the  coil.  The  e.m.f.  in  this  case,  as  in  the  previous 
one,  will  depend  upon  the  rapidity  of  the  movement  of  the 
magnetic  field  with  respect  to  the  coil,  or  vice  versa. 

If  the  number  of  turns  of  wire  composing  the  coil  be 
increased  or  decreased,  there  will  be  a  corresponding  increase 
or  decrease  in  the  e.m.f.  induced  in  the  winding  due  to  a 
given  movement  of  the  coil  or  magnet  with  respect  to  the 
other.  The  induced  e.m.f.  in  the  various  turns  all  act  in 
the  same  direction,  they  are  all  equal,  and  the  resultant 
e.m.f.  is  equal  to  their  sum. 

116.  Magnitude  of  the  Induced  E.M.F.  and  Factors  upon 
Which  It  Depends. — From  the  discussion  in  the  two  previous 
sections  it  is  seen  that  the  induced  e.m.f.  in  a  circuit  de- 
pends upon  the  following  factors: 

(a)  The  rate  of  movement  of  the  conductor  and  the  mag- 
netic field  with  respect  to  each  other.     The  more  rapid 
the  movement  the  greater  the  e.m.f.  induced,  all  other 
quantities   remaining   constant. 

(b)  The  strength  of  the  magnetic  field  or  the  number  of 
lines   of   force    per   square   centimeter.     The   stronger 
the    field    the    greater    the    e.m.f.    induced,    all    other 
quantities  remaining  constant. 

(c)  Upon  the  angle  the  path,  in  which  the  conductor  moves, 
makes  with  the  direction  of  the  lines  of  force.     The 
nearer  this  path  is  to  being  perpendicular  to  the  mag- 
netic field  and  the  position  of  the  conductor,  the  greater 
the  induced  e.m.f. 

(d)  The  length  of  the  wire  that  is  actually  in  the  magnetic 
field.    The  more  wire  there  is  in  the  magnetic  field,  the 
greater  the  induced  e.m.f. 

The  above  facts  can  be  condensed  into  the  following 
simple  statement:  The  magnitude  of  the  induced  e.m.f. 
in  any  circuit  depends  upon  the  rate  at  which  the  conductor, 


ELECTEOMAGNETIC  INDUCTION  1Q7 

forming  part  of  the  circuit,  cuts  magnetic  lines  of  force;  that 
is,  it  depends  upon  the  total  number  of  lines  of  force  cut  per 
second  by  the  conductor.  When  the  conductor  cuts  one  hun- 
dred million  (100  000  000)  lines  in  each  second  during  its  mo- 
tion, an  electrical  pressure  of  one  volt  is  induced  in  the  con- 
ductor. If  the  conductor  cuts  lines  of  force  at  the  rate  of 
two  hundred  million  (200  000  000)  in  each  second,  the  in- 
duced pressure  is  equal  to  two  volts;  and  if  the  conductor  cuts 
eleven  thousand  million  (11  000  000  000)  lines  in  each  second, 
there  will  be  an  induced  e.m.f.  of  110  volts.  If  the  circuit  of 
which  this  conductor  forms  a  part  be  closed,  there  will  be  a 
current  in  the  conductor,  which  has  a  strength  equal  to  the 
induced  pressure  divided  by  the  total  resistance  of  the 
circuit. 

Example. — A  conductor  cuts  across  a  magnetic  field  of 
110  000  000  lines  of  force  100  times  per  second.  (The  con- 
ductor always  moves  across  the  field  in  the  same  direction.) 
How  many  volts  are  induced  in  the  wire? 

Solution. — A  conductor  cutting  11 000  000  lines  of  force 
100  times  per  second  would  be  equivalent  to  cutting 
(11000000X100),  or  1100000000  lines  once  per  second. 
Cutting  1 100  000  000  lines  of  force  per  second  will  induce  in 
a  conductor  (1 100  000  000 -i- 100  000  000),  or  11  volts. 

Ans.     11  volts. 

117.  Direction  of  Induced  E.M.F. — From  the  previous  dis- 
cussion it  is  seen  that  the  direction  of  the  induced  e.m.f. 
depends  upon  the  direction  of  the  magnetic  field  and  the 
direction  in  which  the  conductor  is  moved  with  respect  to 
the  field. 

If  a  piece  of  copper  be  bent  into  the  form  shown  by 
(ECDF),  Fig.  75,  and  a  second  piece  (AB)  be  placed  across 
the  first  and  the  combination  placed  in  a  magnetic  field  as 
shown  by  the  vertical  arrows  in  the  figure,  there  will  be  a 
current  around  the  metallic  circuit  thus  formed  when  the  con- 
ductor (AB)  is  moved  to  the  right  or  to  the  left  of  its  initial 
position.  When  the  conductor  (AB)  is  moved  it  cuts  across 
some  of  the  lines  of  force  and  there  is  an  induced  pressure  set 
up  in  it  which  .produces  a  current.  The  direction  of  this 
current  will  be  reversed  when  the  direction  of  motion  of 
(AB),  or  the  direction  of  the  magnetic  field,  is  reversed. 


108 


PEACTICAL  APPLIED  ELECTKICITY 


When  the  wire  is  moved  in  the  direction  indicated  by  the 
arrow  (K)  in  the  figure,  the  end  (B)  is  positive  and  the  other 
end  (A)  is  negative,  or  the  potential  of  (B)  is  higher  than  that 
of  (A).  This  difference  in  pressure  between  (B)  and  (A) 
will  cause  a  current  in  the  circuit,  from  (B)  through  (C) 
and  (D)  to  (A)  and  from  (A)  to  (B).  The  wire  (AB)  is  the 
part  of  the  circuit  in  which  the  electrical  pressure  is  gen- 
erated and  the  electricity  passes  from  a  lower  to  a  higher 
potential  through  this  part  of  the  circuit,  just  as  the  elec- 
tricity passes  from  the  negative  to  the  positive  pole  of  the 
battery  through  the  battery  itself. 

A  simple  way  of  determining  the  direction  of  induced 
e.m.f.  in  a  circuit,  when  the  direction  of  motion  of  the  con- 


E    B 


A 

Fig.  75 


Fig.  76 


ductor  and  the  direction  of  the  magnetic  field  are  known,  is 
as  follows:  Suppose  a  conductor  (C),  Fig.  76,  is  moved  to 
the  -right,  as  indicated  by  the  arrow,  in  a  magnetic  field  whose 
direction  is  downward,  as  shown  by  the  small  arrow  heads 
at  the  lower  part  of  the  figure.  The  lines  of  force  might  be 
thought  of  as  elastic  bands  that  are  pushed  aside  when  the 
conductor  is  moved  in  the  field,  but  finally  break  and  join 
again  on  the  left  side  of  the  conductor,  leaving  a  line  linked 
around  the  conductor,  as  shown  by  the  small  circle  (c).  The 
direction  of  this  line  of  force  about  the  conductor  is  clock- 
wise, or  it  corresponds  to  a  line  produced  by  a  current  toward 
the  paper.  Hence,  the  current  in  the  conductor  is  from  the 
observer  toward  the  paper.  It  must  be  remembered  that  the 
current  is  from  a  point  of  relatively  low  potential  to  one  of 
higher  potential  in  this  part  of  the  circuit. 


ELECTROMAGNETIC  INDUCTION 


109 


118.  Rules  for  Determining  Direction  of  Induced  E.M.F. — 
There  are  a  number  of  different  ways  of  remembering  the 
relation  between  the  direction  of  the  electrical  current,  the 
direction  of  the  conductor's  motion,  and  the  direction  of  the 
magnetic  field.  One  of  the  best  rules  is  what  is  known  as 
Fleming's  "Right-Hand  Rule,"  and  it  is  as  follows:  Place 
the  thumb  and  the  first  and  second  fingers  of  the  right  hand 
all  at  right  angles  to  each  other.  Now  turn  the  hand  into 
such  a  position  that  the  thumb  points  in  the  direction  of 
motion  of  the  conductor,  and  the  first  finger  points  in  the 
direction  of  the  lines  of  force,  then  the  second,  or  middle, 
finger  will  point  in  the  direction  of  the  current  that  is  set 
up  in  the  conductor  by  the  induced  pressure.  An  illustra- 
tion of  the  "Right-Hand  Rule"  is  shown  in  Fig.  77. 


Inducedemf 
Fig.  77 


Fig.  78 


119.  Primary  and  Secondary  Coils.— If  a  coil  of  wire 
be  connected  in  series  with  a  galvanometer  (G),  as  shown  in 
Fig.  78,  and  a  second  coil  (C2)  that  has  its  winding  con- 
nected to  a  battery  (B)  be  moved  into  or  out  of  the  coil 
(Ci),  there  will  be  a  deflection  produced  on  the  galvanometer, 
just  as  though  a  permanent  magnet  had  been  used  instead  of 
the  coil  (C2).  The  coil  (Cj),  in  which  the  induced  e.m.f.  is 
produced,  is  called  the  secondary  and  the  coil  (C2),  in  which 
the  inducing  current  exists,  is  called  the  primary. 

There  are  a  number  of  different  ways  of  producing  an 
induced  e.m.f.  in  the  secondary  coil  besides  moving  one  coil 
with  respect  to  the  other.  Four  of  'these  methods  are  as  fol- 
lows: (Both  coils  are  stationary  and  one  surrounds  the 
other,  or  they  are  both  wound  around  the  same  magnetic  cir- 
cuit). 

(a)     By  making  or  breaking  the  primary  circuit. — Imagine 


HO  PRACTICAL  APPLIED  ELECTRICITY 

two  conductors  (AB)  and  (CD),  Fig.  79,  that  are  parallel  to 
each  other  and  very  near  together  but  are  connected  in 
two  electrically  independent  circuits.  The  conductor  (AB) 
is  in  series  with  the  galvanometer  (G)  and  constitutes  the 
secondary  circuit.  The  conductor  (CD)  is  connected  in  se- 
ries with  a  battery  (B)  and  a  switch  (S)  that  can  be  used 
in  opening  and  closing  the  primary  circuit.  When  the  primary 
circuit  is  completed  by  closing  the  switch  (S),  there  will  be 
a  current  through  the  conductor  (CD)  from  (C)  to  (D), 
This  current  will  produce  a  magnetic  field  about  its  path 
and  the  field  around  the  conductor  (CD)  will  cut  the  con- 
ductor (AB)  which  will  result  in  an 
induced  e.m.f.  being  set  up  in  the 
secondary  circuit  that  will  send  a 
current  through  the  circuit  from  (B) 
to  (A).  The  direction  of  this  in- 
duced e.m.f.  can  be  determined  by 


means    of    the    "Right-Hand    Rule." 


B  ' 

L_|  |J  d  | — ^^  \ — )      There  will  be  an  e.m.f.  set  up  in  the 

secondary  for  a  period  of  time  cor- 

Fis-  79  responding  to  the  time  required   to 

establish  the  current  in  the  primary. 

As  soon  as  the  primary  current  ceases  to  change  in  value, 
there  will  be  no  movement  of  the  magnetic  field  and  the  con- 
ductor TAB)  with  respect  to  each  other. 

If  now  the  primary  circuit  be  broken,  the  magnetic  field 
surrounding  the  conductor  (CD)  will  collapse,  and  as  a  result 
the  conductor  (AB)  will  cut  the  field  again,  but  in  the  oppo- 
site direction  to  what  it  did  when  the  current  in  the  circuit 
(CD)  was  being  established.  There  will  be  a  current  pro- 
duced in  the  secondary  that  is  practically  constant  in  dura- 
tion if  the  primary  circuit  is  made  and  broken  a  sufficient 
number  of  times.  The  conductors  forming  the  primary  and 
secondary  circuits  are  usually  wound  into  coils,  and  they 
may  be  placed  side  by  side  or  one  outside  the  other.  The 
e.m.f.  induced  in  the  secondary,  due  to  a  certain  change  of 
current  in  the  primary,  can  be  greatly  increased  by  winding 
the  two  coils  on  an  iron  core.  The  magnetic  field  that 
passes  through  the  two  windings,  due  to  the  current  in  the 
primary  is  a  great  deal  stronger  when  they  are  placed  on 
the  iron  core  than  it  is  when  an  air  core  is  used  and,  as  a 


ELECTEOMAGNETIC  INDUCTION 


111 


O  o=^0=CD 

Secondary] 

\£/V/V/V  I         i 


result,  a  greater  number  of  lines  of  force  will  cut  the  second- 
ary winding  when  the  primary  circuit  is  completed  or  broken. 

The  induction  coil  consists  of  two  windings,  a  primary  and 
a  secondary,  placed  upon  an  iron  core  with  some  sort  of 
a  device  connected  in  the  primary  circuit  for  interrupting 
the  primary  current.  See  Fig.  80.  The  relation  between  the 
primary  and  the  secondary  e.m.f.  is  practically  the  same  as  the 
relation  between  the  number  of  turns  of  wire  in  the  primary 
and  in  the  secondary  windings. 

(b)  Varying  the  strength  of  current  in  the  primary. — This 
in  reality  is  practically  the  same  as  the  previous  method, 
except  the  circuit  is  not  entirely  broken.  Any  change  in  the 
value  of  the  primary  current  will  result  in  a  change  in  the 
magnetic  field  surrounding 
the  primary  winding,  and 
as  this  field  expands  or 
contracts  it  will  cut  the 
conductor  composing  the 
secondary  and,  as  a  result, 
there  will  be  an  induced 
e.m.f.  set  up  in  the  sec- 
ondary winding.  The  di- 
rection of  this  induced  III1  r ' 
e.m.f.  will  depend  upon 

whether    the    field    is    ex-  Fig.  80 

panding     or      contracting, 

which,  in  turn,  depends  upon  the  change  of  current  in  the 
primary  —  whether  it  be  increasing  or  decreasing.  The 
telephone  induction  coil  is  a  good  application  of  this 
means  of  producing  an  alternating  current  in  the  secondary 
due  to  a  change  in  the  value  of  the  current  in  the  primary. 
The  connections  of  a  telephone  coil  are  shown  in  Fig.  81. 
(S)  and  (P)  represent  the  secondary  and  the  primary  wind- 
ings of  the  induction  coil,  which  are  usually  wound,  one  out- 
side of  the  other,  on  an  iron  core  composed  of  a  bundle  of 
small  iron  wires.  (R)  is  the  receiver  that  is  connected  in 
series  with  the  telephone  line  and  the  secondary  winding.  The 
transmitter  (T)  is  connected  in  series  with  the  battery  (B) 
and  the  primary  winding.  The  construction  of  the  trans- 
mitter is  such  that  when  the  air  is  set  in  vibration  about  the 
transmitter,  due  to  any  cause,  there  will  be  a  change  in  the 


112 


PRACTICAL  APPLIED  ELECTEICITY 


Pig.  81 


value  of  the  resistance  it  offers  to  the  current  in  the  circuit 
of  which  it  is  a  part.  The  vibration  of  the  air  then  causes 
a  varying  current  through  the  primary  winding  of  the  induc- 
tion coil,  which,  in  turn,  produces  an  e.m.f.  in  the  secondary 
winding  and  as  a  result  of  this  e.m.f.  there  will  be  a  current 
over  the  telephone  line  that  produces  an  effect  on  the  re- 
ceivers both  at  the  sending  and  the  receiving  stations.  It  must 
be  understood  that  the  diagram,  Fig.  81,  does  not  show  the 
complete  circuit  of  the  telephone. 

(c)  Reversing  the  cur- 
rent in  the  primary. — If  a 
switch  were  constructed 
so  that  its  operation  would 
reverse  the  current  in  the 
primary  winding,  there 
would  be  an  e.m.f.  induced 
in  the  secondary  winding 
due  to  a  change  in  the 
magnetic  field  surrounding 
the  two  windings.  This 

method  is  applied  in  practice  in  what  is  called  a  transformer. 
The  switch,  however,  is  not  used,  as  the  current  in  the  pri- 
mary winding  is  an  alternating  current — a  current  that  is  re- 
versing in  direction  at  regular  intervals.  The  operation  of  the 
transformer  will  be  taken  up  under  the  subject  "Alternating 
Current." 

(d)  Moving  the  iron  core  about  which  the  windings  are 
placed. — The  magnetic  field  produced  by  a  given  value  'of 
current  in  the  winding  of  a  coil  will  depend  upon  the  kind  of 
material  composing  the  magnetic  circuit,  whether  it  be  a 
material  of  high  or  low  permeability.  If  the  iron  core  upon 
which  the  windings  are  placed  be  moved  so  as  to  increase  the 
reluctance  in  the  magnetic  circuit,  there  will  be  a  decrease 
in  the  lines  of  force,  and,  as  a  result,  there  will  be  an  induced 
e.m.f.  set  up  in  the  secondary  winding.  If  the  core  be  moved 
so  as  to  decrease  the  reluctance  of  the  circuit,  there  will  be 
an  increase  in  the  number  of  magnetic  lines,  or  an  increase 
in  field  strength,  and  an  induced  e.m.f.  will  be  produced 
in  the  secondary  winding  in  the  opposite  direction  to  that 
produced  when  the  field  strength  decreased.  This  principle 
is  employed  in  what  is  called  the  inductor  type  of  alternating- 


ELECTROMAGNETIC  INDUCTION 


113 


current  generator.  An  e.m.f.  is  produced  by  rotating  iron 
poles  between  the  primary  and  the  secondary  windings,  which 
changes  the  number  of  the  lines  of  force  through  the  sec- 
ondary due  to  the  current  in  the  primary. 

120.  Mutual    Induction. — The  reaction  of  two  independent 
electrical  circuits  upon  each  other  is  called  mutual  induction. 
These  circuits  of  course  must  be  so  placed  with  respect  to 
each   other  that  the   magnetic   field   due   to   the   current   in 
either  of  them  will  produce  an  effect  in  the  other.     A  good 
practical  example  of  mutual  induction  is  that  of  a  telephone 
wire    that    runs    parallel    to,    say,    an    electric-light    circuit. 
The  magnetic  field  surrounding  the  electric-light  circuit  cuts 
the  telephone  conductor  and  sets  up  in  it  an  induced  e.m.f. 
This    induced    e.m.f.    will 

produce  a  current  in  the 
telephone  circuit  which  in- 
terferes with  the  satisfac- 
tory operation  of  the  tele- 
phone line.  Often  the 
conversation  on  one  tele- 
phone circuit  can  be  heard 
on  another  circuit  due  to 

this  same  cause.  The  wires  composing  the  circuits  should  have 
their  positions  interchanged,  as  shown  in  Fig.  82.  The  e.m.f.'s 
induced  in  the  two  wires  composing  the  telephone  circuit  are 
opposite  in  direction  with  respect  to  the  telephone  circuit 
and  they  will  all  exactly  neutralize  each  other  when  the  two 
wires  are  properly  changed  in  position.  The  changing  of  the 
position  of  two  wires  is  called  a  transposition. 

121.  Self-Induction. — If  the  value  of  the  current  in  a  wire 
forming  a  coil  be  changed  in  any  way,  there  will  be  a  change 
in  the  strength  of  the  magnetic  field  surrounding  the  wire. 
This  change  in  strength  of  the  magnetic  field  will  produce  an 
e.m.f.  in  the  conductor  in  which  the  current  is  changing  just 
the  same  as  though  the  field  were  changed  in  strength  by  a 
current  in  an  independent  electrical  circuit.     This  cutting  of 
the   wire   by   the   magnetic    field    produced    by   a    current   in 
the  wire  itself  is  called  self-induction.     When  a  coil  carry- 
ing a  current  has  its   circuit  broken,  there  will  be  a  spark 
formed  at  the  break  due  to  the  induced  e.m.f.     This  induced 
e.m.f.  will  depend  upon  the  form  of  the  coil  and  the  kind 


Tel 
^—  a  —  > 

i         > 

uit 
k—  a  —  v 

ephoneCirc 

k  '          sa  > 
Fig.   82 

114 


PRACTICAL  APPLIED  ELECTRICITY 


of  material  associated  with  the  coil.  A  straight  conductor 
will  have  a  small  e.m.f.  induced  in  it  when  the  circuit  is 
broken,  as  the  magnetic  field  surrounding  the  conductor  is 
not  very  strong.  If  the  conductor  be  bent  into  a  coil  the 
induced  e.m.f.  will  be  greater  than  that  for  the  straight 
conductor,  as  very  nearly  all  the  magnetic  lines  of  force 
produced  by  each  turn  cut  all  the  other  turns  composing  the 
coil,  and  the  total  number  of  lines  that  cut  the  winding  is 
greatly  increased.  This  induced  e.m.f.  can  be  further  in* 
creased  by  providing  the  coil  with  an  iron  core,  which  in- 
creases the  field  strength  due  to  a  given  current  in  the 
winding. 

In  electric-gas  lighting  it  is  desired 

r-  --' — ,          to  have  a  circuit  of  large  self-induc- 

tion so  that  there  will  be  a  good 
spark  formed  when  the  circuit  is 
broken  at  the  gas  jet.  The  heat  of 
this  spark  is  sufficient  to  ignite  the 
gas.  The  self-induction  of  such  a 
circuit  is  increased  by  connecting  in 
series  with  the  battery  and  other 
parts  of  the  circuit  a  coil  wound  upon 
an  iron  core.  This  kind  of  a  coil  is 
often  spoken  of  as  a  "kick  coil." 

If  a  lamp  (L)  be  connected  across 
the  terminals  of  an  electromagnet 
(M),  as  shown  in  Fig.  83,  the  lamp  will 

burn  very  bright  just  for  an  instant  after  the  battery  circuit  is 
opened.  This  is  due  to  the  induced  e.m.f.  set  up  in  the  winding 
of  the  electromagnet  when  the  field  contracts  and  cuts  the 
various  turns.  The  e.m.f.,  of  course,  is  only  momentary,  as  the 
field  soon  disappears  when  the  circuit  is  broken  by  opening 
the  switch  (S).  The  voltage  the  lamp  is  constructed  to 
operate  on  and  the  battery  voltage  should  be  practically  the 
same  in  order  to  give  the  best  results. 

122.  inductance. — The  inductance  of  any  circuit  depends 
upon  the  form  of  the  circuit  and  the  kind  of  material  sur- 
rounding the  circuit.  There  is  an  increase  in  the  value  of  the 
inductance  of  a  coil  with  an  increase  in  the  number  of  turns 
and  an  increase  in  the  permeability  of  the  material  com- 
posing the  magnetic  circuit.  A  coil  is  said  to  have  unit 


Fig.  83 


ELECTKOMAGNETIC  INDUCTION  115 

inductance  when  an  induced  e.m.f.  of  one  volt  will  be  produced 
due  to  a  change  in  the  current  in  the  winding  of  one  ampere 
in  one  second.  That  is,  if  the  current  changes,  say,  from 
two  to  three  amperes  in  one  second  and  there  is  an  induced 
e.m.f.  of  one  volt,  the  coil  is  said  to  have  unit  inductance. 
The  unit  of  inductance  is  the  henry,  and  inductance  is  usually 
represented  by  the  symbol  (L). 

The  inductance  of  any  coil  can  be  calculated  by  the  use 
of  the  following  equation  when  the  dimension  of  the  coil 
and  other  quantities  are  known: 


(82) 


109  X  I 


In  the  above  equation  (n)  is  the  number  of  turns  of  wire 
on  the  coil,  (ju)  is  the  permeability  of  the  material  composing 
the  magnetic  circuit,  (A)  is  the  area  of  the  magnetic  circuit 
in  square  centimeters,  and  (Z)  is  the  length  of  the  magnetic 
circuit  in  centimeters. 

123.  Lentz's  Law.  —  A  careful  consideration  of  the  ways  by 
which  induced  currents  may  be  produced,  whether  it  be  due 
to  self  or  mutual  induction,  will  result  in  the  following  sim- 
ple fact.  In  all  cases  of  electromagnetic  induction,  the  cur- 
rent produced  by  the  induced  e.m.f.  will  always  be  in  such  a 
direction  as  to  tend  to  stop  the  cause  producing  it.  Thus, 
if  a  magnet  be  moved  toward  a  coil,  the  current  in  the  coil 
will  be  in  such  a  direction  that  the  side  of  the  coil  toward 
the  magnet  will  be  of  the  same  polarity  as  the  end  of  the 
magnet  toward  the  coil.  This  results  in  the  induced  current 
tending  to  stop  the  motion  of  the  magnet.  When  the  magnet 
is  moved  away  from  the  coil,  the  current  in  the  coil  will  be 
in  the  opposite  direction  to  what  it  was  before  and  the 
side  of  the  coil  toward  the  magnet  is  of  the  opposite  polarity 
to  the  end  of  the  magnet  toward  the  coil,  and  as  a  result 
they  attract  each  other,  which  tends  to  prevent  the  magnet 
being  moved. 

If  a  coil  of  wire  (Cj),  in  which  there  is  a  current,  be  moved 
toward  a  second  coil  (C2),  that  is,  connected  in  series  with 
a  galvanometer  (G),  Fig.  84,  there  will  be  an  induced  e.m.f. 
set  up  in  the  coil  (C2),  which  will  cause  a  current  through 


116  PRACTICAL  APPLIED  ELECTRICITY 

the  galvanometer  and  thus  produce  a  deflection  of  its  needle. 
The  current  produced  in  the  second  coil  (C2)  will  be  in  such 
a  direction  as  to  make  the  sides  of  the  two  coils  toward  each 
other   of   the    same   polarity.     These   two   poles    repel    each 
other  and  thus  there  is  a  force  opposing  the  movement  of  the 
coils  toward  each  other.    When  the  coil  (C^  is  moved  away 
from  (C2),  the  sides  of  the  two  coils 
adjacent  to  each  other  are  of  opposite 
polarity  and  they  attract  each  other. 
This  results  in  a  force  which  tends  to 
prevent    the    coils    moving   apart.      It 
must  be  remembered  that  this  force 
of  attraction  or  repulsion  between  the 
two  coils  is  present  only  when  there 
F[s-  84  is  a  current  in  both  coils. 

If  the  two  coils  be  wound  on  an  iron 

core  and  the  value  of  the  current  in  the  primary  winding  be 
changed,  there  will  be  a  current  in  the  secondary  in  such  a 
direction  as  to  oppose  any  change  in  the  value  of  the  magnetic 
field  produced  by  the  current  in  the  primary. 

124.     General    Rules  for   Direction   of   Induced   Pressures. — 

(a)  If  a  primary   coil  be  moved  into  a  secondary  coil,  the 

current  in  the  secondary,  due  to  the  induced  e.m.f., 
will  be  in  the  opposite  direction  to  the  primary  current. 

(b)  If  a  primary  coil  be  moved  out  of  a  secondary  coil,  the 

current  in  the  secondary,  due  to  the  induced  e.m.f.,  will 
be  in  the  same  direction  as  the  primary  current. 

(c)  Where  the  current  is  increasing  in  value  in  the  primary 

coil,  there  will  be  a  current  in  the  secondary  coil,  due 
to  the  induced  e.m.f.  that  is  in  the  opposite  direction 
to  that  in  the  primary  coil. 

(d)  When  the  current  is  decreasing  in  value  in  the  primary 

coil,  there  will  be  a  current  in  the  secondary  coil, 
due  to  the  induced  e.m.f.  that  is  in  the  same  direction 
as  that  in  the  primary  coil. 

In  the  above  cases  the  secondary  is  closed.  If  the  secondary 
be  open  there  will  be  an  induced  e.m.f.  set  up,  which  would 
produce  a  current  in  the  direction  indicated  above,  if  the 
circuit  was  closed.  Rules  (c)  and  (d)  apply  when  the 


ELECTROMAGNETIC  INDUCTION 


117 


primary  and  the  secondary  are  stationary  and  the  current  is 
changing  in  value  in  the  primary. 

125.  Eddy  Currents. — If  a  disk  of  copper,  or  other  conduct- 
ing material,  be  rotated  below  a  suspended  magnet,  as  shown 
in  Fig.  85,  currents  will  be  produced  in  the  disk,  which  cir- 
culate in  paths  similar  to  those  shown  by  the  dotted  lines 
in  the  figure.  These  currents  tend  to  oppose  the  motion  pro- 
ducing them  and,  as  a  result,  the  magnet,  if  it  is  free  to  move, 


B, 


Fig.   85 


Fig.   86 


will  be  rotated  in  the  same  direction  as  the  disk.  If,  how- 
ever, the  magnet  is  held  in  position  and  the  disk  is  rotated,  a 
greater  force  must  be  applied  to  cause  the  disk  to  rotate  than 
is  required  when  the  magnet  is  free  to  turn. 

Currents  induced  in  masses  of  metal  that  are  moved  in  a 
magnetic  field,  or  are  cut  by  a  moving  magnetic  field,  are 
called  eddy  currents. 

Faraday's  dynamo,  as  shown  in  Fig.  86,  consisted  of  a  disk 

'  of   copper    (D)    rotated   between   the   poles   of   a   permanent 

magnet   (M),  the  electrical  connection  to  the  machine  being 

made  by  means  of  brushes  (Bj)  and  (B2)  that  rested  upon  the 

center  and  edge  of  the  disk. 

126.  Application  of  Eddy  Currents. — A  good  example  of 
the  practical  application  of  the  fact  that  eddy  currents  are 
set  up  in  a  mass  of  metal  revolved  in  a  magnetic  field,  is  found 
in  almost  all  types  of  integrating  wattmeters.  A  disk  of  copper 


118 


PRACTICAL  APPLIED  ELECTRICITY 


is  fastened  on  the  same  shaft  as  the  rotating  portion  of  the 
meter  is  mounted  upon,  and  this  disk  revolves  between  the 
poles  of  several  permanent  magnets,  as  shown  in  Fig.  87. 
This  combination  of  disk  and  magnets  constitutes  a  small 
generator  and  serves  as  a  load  for  the  motor  part  of  the 
meter.  The  torque  required  to  drive  the  disk  in  the  field 

of  the  magnets  is  propor- 
tional to  the  speed,  and 
since  the  driving  torque  of 
the  motor  is  proportional 
to  the  product  of  the  im- 
pressed voltage  and  the 
load  current,  or  the  watts, 
the  speed  of  the  moving 
part  of  the  meter  must  be 
proportional  to  the  watts. 
The  integrating  meter  will 
be  taken  up  more  in  detail 
In  the  chapter  on  "Electric- 
al Measuring  Instruments." 
127.  Eddy-Current  Loss. 
— The  energy  expended  in 
producing  eddy  currents 
is  converted  into  heat  and 
represents  a  loss.  These 
losses  are  quite  large  in 
dynamos,  motors,  trans- 
formers, etc.,  and  it  is 
always  best  to  reduce 
Fig.  87  them  to  a  minimum  when 

it   is    possible.      The   best 

way  of  reducing  them  is  to  split  the  mass  of  metal  up  into 
sheets,  the  plane  of  these  sheets  being  parallel  to  the  direction 
of  the  lines  of  force.  It  is  customary  to  build  up  all  volumes 
of  metal  that  are  likely  to  have  eddy  currents  produced  in 
them  from  thin  sheets,  or  laminations,  as  they  are  called. 
Induction-coil  cores  are  made  from  short  lengths  of  small  wire 
instead  of  using  a  solid  core.  Armature  cores  and  the  cores  of 
transformers  are  laminated  so  as  to  reduce  the  loss  due  to 
eddy  currents.  These  laminae  are  usually  between  .014  and 
.025  inch  in  thickness  for  dynamos,  and  the  space  between 


ELECTKOMAGNETIC  INDUCTION  119 

them  that  is  taken  up  by  the  oxide  that  forms  on  their  surface 
is  about  .002  inch.  Losses  due  to  eddy  currents  could  be  re- 
duced to  an  inappreciable  value  by  decreasing  the  thickness  of 
the  laminae,  but  there  is  a  practical  limit  on  account  of  the 
decrease  in  effective  iron  area,  caused  by  the  waste  of  space 
taken  up  by  the  insulation  between  adjacent  lamin.ne. 

When  the  laminae  are  perfectly  insulated  from  each  other, 
the  following  equation  can  be  used  in  calculating  the  power 
in  watts  lost  in  iron  due  to  eddy  currents: 

We  =  k  X  V  X  f2  x  t2  x  £2  (83) 

In  the  above  equation  (k)  is  a  constant,  depending  upon 
the  resistance  of  the  iron  per  cubic  centimeter,  which  is 
usually  about  1.6  X  10-H;  (V)  is  the  volume  of  the  iron  in 
cubic  centimeters;  (t)  is  the  thickness  of  one  lamina  in 
centimeters;  (f)  is  the  frequency  of  magnetic  cycles  per 
second;  and  (/3)  is  the  maximum  number  of  lines  per  square 
centimeter  to  which  the  iron  is  magnetized. 

Example.  —  Find  the  eddy-current  loss  in  1000  cubic  centi- 
meters of  iron,  composed  of  laminations  .04  cm.  thick  (in- 
cluding insulation),  that  is  subject  to  a  maximum  (/3)  of 
10  000  lines  per  square  centimeter  and  a  frequency  of  60 
cycles  per  second. 

Solution.—  Taking  the  value  of  (k)  =  1.6  X  10-n  and  sub- 
stituting in  equation  (83)  gives 

1000  X  602  X  (.04)2  x  10  0002 


1.6  X  1011 
1000  X  3600  X  .0016  X  100  000  000 


We  = 


1.6  X  1011 


Ans.     3.6  watts. 

128.  Non-inductive  Circuit. — In  the  construction  of  certain 
coils  it  is  desired  to  have  them  as  nearly  non-inductive  as 
possible.  This  is  accomplished  by  winding  the  coil  with  two 


120 


PEACTICAL  APPLIED  ELECTKICITY 


wires  laid  side  by  side,  as  shown  in  Fig.  88,  their  inner  ends 
being  joined   electrically.     When  the   winding  is   completed, 
the  two  outside  ends  form  the  terminals  of  the  coil.    The  cur- 
rent in  such  a  coil  is  in  one  direction  in  one- 
half  of  the  turns  and  in  the  remaining  half 
of  the  turns  in  the  opposite  direction.     The 
result   is   that   the   magnetic   effect   of   the 
current   in   one-half  of   the   turns   is   equal 
and    opposite    to   the   other   half   and   they 


Fig.  88 


exactly  neutralize,  and  the  inductance  of  the  coil  will  be  zero, 
or  the  coil  will  be  non-inductive. 


CHAPTEE  VIII 

ELECTRICAL    INSTRUMENTS    AND    EFFECTS    OF    A 
CURRENT 

129.  Classification  of  Instruments. — No  attempt  will  be  made 
in  this  chapter  to  describe  all  of  the  various  forms  of  instru- 
ments on  the  market  at  the  present  time,  it  being  deemed 
best  to  confine  the  description  in  almost  every  case  to 
those  that  are  in  most  common  use.  Electricity  is  not  a 
material  substance  like  water  and  cannot  be  measured  in 
the  same  way  since  it  has  no  dimensions  such  as  length, 
breadth,  or  weight.  An  electrical  current  is  studied  and  meas- 
ured by  the  effects  it  produces  in  an  electrical  circuit.  The 
operation  of  all  instruments  depends  upon  some  effect  pro- 
duced by  the  current  and  this  leads  to  the  classification  of 
instruments  into  four  groups  depending  upon  the  particular 
effect  employed  in  their  operation.  These  effects  are: 

(a)  Electro-chemical   effect. 

(b)  Magnetic  effect. 

(c)  Heating  effect. 

(d)  Electrostatic  effect. 

Note:  The  electrostatic  effect  is  not  an  effect  of  a  cur- 
rent primarily,  but  of  electrical  pressure. 

In  addition  to  the  above  classification,  instruments  may 
be  divided  into  the  following  groups: 

(a)  Instruments  suitable  for  direct-current  measurements 
only. 

(b)  Instruments  suitable  for  alternating-current  measure- 
ments only. 

(c)  Instruments  suitable  for  both  direct-  and  alternating- 
current   measurements. 

In  the  following  discussion  of  instruments,  they  will  be 
grouped  according  to  the  effect  upon  which  their  operation 

121 


122 


PRACTICAL  APPLIED  ELECTRICITY 


depends,  and  their  adaptability  to  the  measurement  of  direct 
or  alternating  current  will  be  pointed  out  at  the  same  time. 

Ammeters,  Galvanometers,  and  Voltmeters 

130.  Distinction  between  Ammeters,  Galvanometers,  and 
Voltmeters. — An  ammeter  is  an  instrument  to  be  used  in 
measuring  the  current  in  a  circuit,  and  for  that  reason  am- 
meters will  always  be  connected  in  series  with  that  part  of 
the  circuit  in  which  it  is  desired  to  ascertain  the  value  of 
the  current. 

A  galvanometer  is  an  instrument  used  in  detecting  the 
presence  of  a  current  in  a  circuit,  or  for  measuring  the 
value  of  the  current.  It  is  really  the  same  as  an  ammeter 
as  far  as  construction  and  operation  are  concerned,  but 
it  is  usually  used  in  measuring  very  small  currents  as  com- 
pared to  those  measured  by  ammeters. 


Fig.  89  Fig.  90 

In  Fig.  89,  the  ammeter  (A)  is  connected  in  series  with 
the  battery  (B)  and  the  two  resistances  (Ri)  and  (R2), 
which  are  in  parallel.  The  ammeter  in  this  case  reads 
the  total  current  in  the  main  circuit  but  it  does  not  give 
the  current  in  either  of  the  resistances  (R!>  or  (R2).  If, 
however,  the  instrument  be  connected,  as  shown  in  Fig.  90, 
it  will  indicate  the  current  in  the  resistance  (Ri).  By  chang- 
ing the  instrument  to  the  branch  containing  the  resistance 
(R2),  the  current  in  this  branch  can  likewise  be  determined. 

A  voltmeter  is  an  instrument  for  measuring  the  difference 
in  electrical  pressure  between  any  two  points  to  which 
its  terminals  may  be  connected.  Thus,  if  it  is  desired  to 
know  the  difference  in  electrical  pressure  between  the  ter- 


ELECTKICAL  INSTRUMENTS  123 

minals  of  any  part  of  an  electrical  circuit,  such  as  the  differ- 
ence in  pressure  between  the  terminals  of  a  lamp  that  is 
connected  to  some  source  of  electrical  energy,  as  shown  in 
Fig.  91,  the  voltmeter  is  connected  to  the  two  terminals  and 
its  indication  is  a  measure  of  the  pressure  over  the  lamp.  The 
ammeter  and  the  voltmeter  both  operate  on  the  same  prin- 
ciple, that  is,  their  indications  depend  upon  the  current  pass- 
ing through  them.  The  voltmeter  indication  depends  upon  the 
pressure  between  its  terminals,  because  the  current  through 
it  varies  with  this  difference  in  pressure,  the  resistance  of 
the  instrument  remaining  constant. 

The  resistance  of  an  ammeter  should  be  very  low  for  the 
following  reason:  An  ammeter  will  always  be  connected 
directly  in  the  circuit  and  there  will  be  a  difference  in  elec- 
trical pressure  between  its  terminals  when  there  is  a  cur- 
rent through  it,  which  is  at  any  instant  numerically  equal 
to  the  product  of  the  current  and  the  resistance  of  the  instru- 
ment. This  drop  across  the  ammeter  should  be  small  in 
order  that  the  power  required  to  operate  the  instrument  be 
low  in  value,  it  being  equal  to  the  product  of  the  current 
through  the  ammeter  and  the  difference  in  pressure  between 
ammeter  terminals.  If  the  ammeter  in  Fig.  89  had  a  resist- 
ance whose  value  was  something  near  the  value  of  the  com- 
bined resistance  of  the  two  coils  (Rj)  and  (R2)  in  parallel, 
practically  half  the  output  of  the  battery  would  be  consumed 
in  the  ammeter  and  would  represent  a  loss.  If,  on  the  other 
hand,  the  ammeter  had  a  very  low  resistance,  a  very  small 
part  of  the  output  of  the  battery  would  be  consumed  in  it. 
The  division  of  the  current  between  the  two  branches  of 
the  circuit  shown  in  Fig.  90  would  be  quite  different  after 
the  ammeter  was  introduced  in  either  branch  to  what  it  was 
before,  if  the  ammeter  had  a  large  resistance.  If  the  am- 
meter had  a  small  resistance  in  comparison  to  that  of  either 
of  the  branches,  the  change  in  the  division  of  the  current 
between  the  two  branches  when  the  ammeter  was  introduced 
in  either  of  them  would  be  a  great  deal  less  than  in  the  pre- 
vious case. 

The  resistance  of  a  voltmeter,  on  the  other  hand,  should  be 
as  large  as  possible  for  the  following  reason:  The  loss 
of  power  in  the  voltmeter  is  equal  to  the  product  of  the 
current  through  it  and  the  difference  in  pressure  between  its 


124 


PRACTICAL  APPLIED  ELECTRICITY 


terminals,  and  since  it  is  to  indicate  the  difference  in  pres- 
sure, the  only  way  this  loss  can  be  reduced  is  to  increase  the 
resistance  of  the  instrument,  which  results  in  a  smaller  cur- 
rent. Suppose  the  voltmeter  (V),  shown  in  Fig.  91,  had  a  re- 
sistance equal  to  that  of  the  lamp  (L),  then  the  power 
required  to  operate  the  voltmeter  would  be  equal  to  that 
required  to  operate  the  lamp,  since  there  would  be  the 
same  value  of  current  in  each,  and  the  same  difference  in 
pressure  between  their  terminals.  This  condition  of  affairs 
would  result  in  a  considerable  loss  and  it  could  be  reduced 
by  increasing  the  resistance  of  the  voltmeter.  An  ammeter 

connected  in  the  line  lead- 
ing from  the  generator 
(G)  .to  this  lamp  would  in- 
dicate the  combined  cur- 


rent in  the  lamp  and  the 
voltmeter  circuits.  Hence, 
in  order  to  get  the  current 
in  the  lamp  circuit,  the 
value  of  the  current  in  the 

circuit   should    be    subtracted    from    the    value    of 
current.      If    the    resistance    of    the    voltmeter    be 


Fig.  91 


voltmeter 
the    total 

large  in  comparison  to  that  of  the  lamp,  the  current  in  its 
circuit  will  be  small  in  comparison  to  the  lamp  current  and 
the  ammeter  indication  will  be  practically  equal  to  that  in  the 
lamp  circuit.  The  above  discussion  leads  to  the  conclusion 
that  an  ammeter  and  a  voltmeter  need  differ  only  in  their 
resistance,  the  principle  of  operation  being  the  same. 

131.  Ammeter  Shunts. — In  the  construction  of  ammeters  it 
is  usually  customary  to  make  them  with  two  circuits  between 
their  terminals.  One  circuit  has  a  very  low  resistance  and 
carries  the  greater  portion  of  the  current  to  be  measured, 
while  the  other  circuit  has  a  comparatively  large  resistance 
and  carries  a  small  current.  The  current  in  the  branch  of 
larger  resistance  usually  produces  the  deflection  of  the  mov- 
ing system  of  the  instrument.  The  other  branch  constitutes 
what  is  termed  the  ammeter  shunt.  The  shunt  and  moving 
system  are  usually  mounted  in  the  same  case,  when  the 
instrument  is  used  in  measuring  currents  ranging  from  a 
very  low  value  to  perhaps  600  amperes.  For  large  currents 
they  are  usually  constructed  separately. 


ELECTEICAL  INSTEUMENTS 


125 


If  the  resistance  of  the  shunt  is  known,  the  current  through 
it  can  be  determined  by  measuring  the  difference  in  pres- 
sure between  its  terminals — by  means  of  a  suitable  voltmeter, 
usually  a  millivoltmeter— and  then  dividing  this  difference 
in  pressure  in  volts  by 
the  resistance  gives  the 
value  of  the  current. 
Instruments  used  on 
switchboards  as  a  rule 
have  their  shunts  con- 
nected directly  in  the 
line,  and  small  leads 
run  from  the  terminals 
of  this  shunt  to  the 
moving  system,  which 
is  mounted  in  a  conven- 
ient place  on  the  face 
of  the  board.  An  instru- 
ment and  its  shunt  are 
chown  in  Fig.  92.  The 
needle  of  this  instru- 
ment comes  to  rest  in 
the  center  of  the  scale 
when  there  is  no  cur- 
rent in  its  winding,  and  the  direction  of  its  deflection  will 
depend  upon  the  direction  of  the  currents  in  the  shunt. 


Fig.  92 


Instruments  Whose  Operation  Depends  Upon  Electro-Chemical 
Effect  of  a  Current 


132.  Electrolysis. — If  two  conducting  plates,  such  as  plati- 
rum,  be  immersed  in  acidulated  water  and  a  current  of  elec- 
tricity be  passed  through  the  solution  from  one  plate  to  the 
other,  the  water  will  be  decomposed  into  its  two  constituents, 
oxygen  and  hydrogen.  Such  a  combination  of  plates  and 
solution  constitutes  what  is  called  an  electrolytic  cell,  and 
the  process  of  decomposing  the  liquid  is  called  electrolysis. 
The  solution  through  which  the  electricity  is  being  conducted 
is  called  the  electrolyte,  and  the  two  plates  that  are  im- 
mersed in  the  solution  are  called  electrodes.  The  plate  by 


126 


PRACTICAL  APPLIED  ELECTRICITY 


which  the  electricity  enters  the  solution  is  called  the  positive 
electrode,  or  anode,  and  the  plate  by  which  the  electricity 
leaves  the  solution  is  called  the  negative  electrode,  or  cathode. 
The  parts  into  which  the  electrolyte  is  decomposed  are 
called  ions.  The  ion  liberated  at  the  positive  electrode  is 
called  the  anion,  and  the  one  liberated  at  the  negative  pole 
is  called  the  oath  ion.  The  vessel,  plates,  and  other  appa- 
ratus used  in  electrolysis  constitute  what  is  termed  a 
voltameter,  when  such  apparatus  is  used  to  measure  quantity 
or  current.  When  water  is  decomposed,  hydrogen  appears 
at  the  negative  plate,  or  it  is  the  cathion,  and  oxygen  ap- 
pears at  the  positive  plate,  or  it  is  the  anion.  A  simple 


Electrolyte 


Cathode 


Fig.   93 


Fig.   04 


electrolytic  cell  is  shown  in  Fig.  93.  The  gas  liberated  at 
the  two  electrodes  in  this  case  passes  off  into  the  air.«  The 
voltameter,  however,  can  be  so  constructed  that  the  liberated 
gas  will  collect  in  an  enclosed  U-shaped  tube,  as  shown  in 
Fig.  94.  The  direction  of  the  current  in  the  circuit  is  indi- 
cated in  the  figure  by  the  arrow.  The  oxygen  will  collect 
in  the  tube  (A)  and  force  the  water  down,  while  the  hydrogen 
will  collect  in  (B)  and  force  the  water  down.  The  weight  of 
the  oxygen  gas  liberated  by  a  certain  quantity  of  electricity 
will  be  about  eight  times  that  of  the  hydrogen  gas,  but  the 
oxygen  gas  will  occupy  only  half  the  space  that  the  hydrogen 
gas  occupies,  since  a  given  volume  of  hydrogen  gas  is 
approximately  one-sixteenth  as  heavy  as  the  same  volume 


ELECTKICAL  INSTRUMENTS  127 

of  oxygen  gas,  and  as  a  result  the  volume  of  gas  collecting 
in  the  (B)  tube  will  be  practically  twice  the  volume  of  gas 
in  the  (A)  tube. 

133.  Electrolysis  of  Copper  Sulphate. — When  a  current  ex- 
ists between  two  platinum  plates  immersed  in  a  solution  of 
copper  sulphate  CuSO4  made  by  dissolving  copper  sulphate 
crystals  (bluestone)  in  water,  the  solution  will  be  broken  up 
by  electrolysis  into  Cu  (metallic  copper)  and  SO4  (sulphion). 
The  hydrogen  gas  liberated  at  the  negative  electrode  takes 
the  place  of  the  Cu  in  the  CuSO4  forming  H2SO4  (sulphuric 
acid)  and  the  Cu  is  deposited  on  the  negative  plate.  Oxygen 
will  be  liberated  at  the  positive  electrode  as  in  the  previous 
case.  All  of  the  Cu  contained  in  the  solution  will  be  de- 
posited on  the  negative  plate  if  the  current  be  allowed 
to  pass  through  the  electrolytic  cell  for  a  considerable  time. 
When  the  Cu  has  all  been  removed  from  the  solution  it  will 
be  practically  colorless.  The  reaction  taking  place  in  the  cell 
can  be  represented  as  follows: 

CuSO4  =  Cu  +  SO4  (84) 

Copper  sulphate  is  decomposed  into  copper  and  sulphion. 
The  Cu  is  deposited  on  the  negative  plate. 

S04  +  H20  =  H2S04  +  O  (85) 

The  sulphion  and  water  combine  forming  sulphuric  acid  and 
oxygen.  The  oxygen  is  liberated  and  passes  off  into  the 
air  and  the  sulphuric  acid  remains  in  the  solution. 

In  the  above  case  the  negative  plate  will  increase  in 
weight  due  to  the  deposit  of  copper  upon  it  and  this  increase 
in  weight  is  proportional  to  the  quantity  of  electricity  pass- 
ing between  the  two  electrodes. 

If  copper  plates  be  substituted  for  the  platinum  plates, 
the  sulphuric  acid  will  attack  the  positive  electrode  and 
just  as  much  copper  will  be  thrown  into  solution  as  is 
deposited  upon  the  negative  electrode.  This  results  in  no 
change  in  the  electrolyte,  but  there  is  a  wasting  away  of  the 
positive  plate  and  an  equal  increase  in  weight  of  the  negative 
plate  as  the  electrolytic  action  continues. 

134.  Electroplating. — The  principles  of  electrolysis  are  ap^ 
plied  in  coating  objects  with  a  layer  of  metal  and  the  proc, 
ess  is  called  electroplating.  The  object  to  be  plated  always 


128  PRACTICAL  APPLIED  ELECTRICITY 

forms  the  cathode  of  the  electrolytic  cell  and  the  metal  to 
be  deposited  is  held  in  solution  and  as  the  process  con- 
tinues metal  is  supplied  to  the  solution  from  a  plate  which 
forms  the  anode  of  the  cell.  This  plate  should,  of  course, 
be  of  the  same  material  as  the  metal  in  the  solution.  All 
articles  cannot  be  coated  with  certain  metals  without  having 
first  been  coated  with  some  other  metal.  As  an  example, 
articles  composed  of  iron,  tin,  lead,  and  zinc  cannot  be  silver- 
or  gold-plated  without  first  being  copper-plated. 

135.  Electrotyping.— An  electrotype  of  a  column  of  stand- 
ing type  is  made  as  follows:     First,  an  impression  in  wax 
is  made,  then  the  surface  of  this  impression  is  dusted  over 
with   powdered   graphite   to   make   the   surface   a   conductor. 
This  mold  is  then  placed  in  a  copper-plating  bath,  it  forming 
the  cathode,  and  receives  a  thin  coating  of  metallic  copper. 
When  sufficient  copper  has  been  deposited,  the  mold  is  re- 
moved from  the  solution  and  the  copper  plate  that  was  formed 
is  separated  from  the  mold  and  backed  with  type  metal  to  a 
thickness  of  about  %  inch,  and  then  mounted  on  a  wooden 
block.     It  is  necessary  to  back  the  copper  plate  with  type 
metal  because  it  is  so  thin  that  it  would  not  stand  the  pres- 
sure to  which  it  is  subjected  in  the  printing  press. 

136.  Polarity    Indicator. — The   polarity  of   a   direct-current 
circuit  can  be  determined  as  follows:     Immerse  the  ends  of 
two  wires  that  are  connected  to  the  line  wires,  whose  polarity 
it  is   desired   to  determine,  into   a   vessel   of  water,   taking 
care  that  the  two  ends  do  not  come  into  contact  with  each 
other.     Since   approximately   twice    as   much   hydrogen    gas 
(by  volume)  is  liberated  at  the  negative  electrode  as  oxygen 
gas  at  the  positive  electrode,  the  polarity  of  the  circuit  being 
tested  is  easily  determined.     A  simple  polarity  indicator  can 
be  constructed  as  follows:      Place  in   a   small   glass  tube  a 
solution  of  iodide  of  potassium,  to  which  a  little  starch  has 
been   added.     Two    short   pieces   of   wire   should   be    sealed 
into  the  ends  of  the  tube.    When  a  current  is  passed  through 
this  solution  iodine  is  liberated  at  the  positive  terminal  and 
the  solution  is  turned  blue  around  this  terminal. 

137.  Prevention  of  Electrolytic  Action. — Electrolytic  action 
is  oftentimes  the  source  of  a  great  deal  of  trouble,  especially 
in    the    deterioration   of   underground   metals,    such    as   gas, 
water,  and  sewer  pipes,  and  the  lead  covering  on  telephone 


ELECTEICAL  INSTRUMENTS  129 

and  power  cables.  Electricity  takes  the  path  of  least  resist- 
ance in  completing  its  circuit  and,  as  a  result,  all  conductors 
that  are  buried  in  the  ground  and  not  insulated  from  it, 
usually  conduct  some  electricity,  especially  in  localities  where 
street  car  and  power  companies  are  operating  with  grounded 
circuits.  There  will  be  no  decomposition  of  the  pipe  or 
lead  sheath  where  the  electricity  flows  onto  them,  but  at  the 
point  where  it  leaves,  an  electrolytic  action  will  take  place 
which  results  in  the  metal  of  the  pipe  or  cable  sheath  being 
carried  away.  This,  of  course,  means  that  the  pipe  or  cable 
sheath  will  be  greatly  damaged  or  completely  destroyed 
if  the  action  is  allowed  to  continue.  To  prevent  this  action, 
one  end  of  a  conductor  is  electrically  connected  to  the  pipe 
or  cable  sheath  at  the  points  where  the  electricity  tends 
to  leave  them  ard  the  other  end  of  the  conductor  is  buried, 
or  grounded.  The  electrolytic  action  still  continues  but  it 
takes  place  at  the  end  of  the  conductor  in  the  ground  and 
the  damage  is  not  serious.  In  some  cases  the  pipes  are 
wrapped  with  an  insulating  tape  or  coated  with  an  insu- 
lating compound,  which  tends  to  prevent  the  electricity  pass- 
ing on  or  off  of  them,  thus  reducing  the  electrolytic  action. 
The  connecting  of  a  cable  sheath  or  pipe  to  the  ground  is 
called  bonding.  Rail  joints  are  bonded  by  connecting  the 
ends  of  the  rails  electrically  by  means  of  a  flexible  copper 
conductor. 

138.  Weight  Voltameter. — Since  the  weight  of  a  metal 
deposited  or  the  weight  of  water  decomposed  by  a  given 
quantity  of  electricity  is  known,  the  electrolytic  cell  may  be 
used  as  a  quantity  measuring  instrument.  Thus,  if  two  cop- 
per plates  be  immersed  in  a  solution  of  copper  sulphate  and 
a  quantity  of  electricity  passed  between  them,  there  will  be  a 
change  in  weight  of  the  two  plates.  This  change  in  weight 
of  the  plates  can  be  determined  and  from  it  the  quantity  of 
electricity  that  passed  between  them  can  be  calculated.  An 
instrument  of  this  kind  can  be  used  in  measuring  the  current 
in  a  circuit,  If  it  remains  constant  in  value  for  a  certain 
time.  Thus,  if  a  unit  quantity  of  electricity  pass  between 
the  two  plates  in  one  second,  there  will  be  a  current  of  one 
ampere  in  the  circuit.  If  ten  units  of  quantity  of  electricity 
pass  between  the  plates  in  ten  seconds,  there  will  still  be  a 
current  of  one  ampere,  or  if  ten  units  of  quantity  pass  in 


130  PRACTICAL  APPLIED  ELECTRICITY 

two  seconds,  there  will  be  a  current  of  five  amperes.  Hence, 
in  order  to  measure  a  current  that  is  constant  in  value,  with 
the  voltameter,  it  is  only  necessary  to  note  the  time  taken 
to  produce  a  certain  deposit.  The  weight  of  the  total  deposit 
divided  by  the  time  gives  the  weight  of  the  deposit  per  sec- 
ond and  this  value  divided  by  the  weight  each  coulomb  will 
deposit  gives  the  current  in  amperes,  since  the  current  is 
the  number  of  coulombs  per  second.  Call  the  total  gain  in 
weight  in  grams  (W),  the  time  in  seconds  taken  to  produce 
the  gain  in  weight  (t),  and  the  deposit  produced  by  one 
coulomb  (K).  Then 

gain  in  weight  in  grams 

Amperes  =  

gain  in  grams  per  coulomb  X  time  in  seconds 
or  (86) 

(87) 


Table  No.  VII  gives  the  weight  in  grams  that  one  coulomb 
or  one  ampere  in  one  second  will  deposit  (called  the  electro- 
chemical equivalent). 


TABLE  NO.  VII 
ELECTRO-CHEMICAL   EQUIVALENTS   IN   GRAMS   PER   COULOMB 

K  for  silver 001118  gram 

K  for  copper 000329  gram 

K  for  zinc    000338  gram 

K  for  lead   001071  gram 

K  for  nickel   000304  gram 

A  commercial  form  of  voltameter  is  shown  in  Fig.  95.  The 
two  outside  plates  form  the  anode  and  they  are  connected 
electrically.  There  will  be  a  metallic  deposit  on  both  sides 
of  the  middle  plate  which  form  the  cathode,  due  to  the  pres- 
ence of  the  two  outside  plates. 

Example. — The  increase  in  weight  of  a  platinum  plate  in 
a  silver  voltmeter  was  4.0248  grams  when  the  circuit  in 
which  the  voltameter  was  connected  was  closed  for  15  min- 
utes. What  current  was  there  in  the  circuit? 


ELECTEICAL  INSTEUMENTS  131 

Solution. — Substituting  in   equation   (87)    gives 
4.0248 


—  =  4 


.001118  X  15  X  60 

Ans.     4  amperes. 

139.  Adaptability  of  Voltameters.— The  voltameter  is  really 
a  quantity-measuring  instrument  and  it  will  only  measure  the 
current  when  the  rate  of  flow  of  electricity  is  constant  and,  as 
a  result,  it  is  not  suitable  for  ordinary  work.  Determinations 


Fig.  95 

of  the  value  of  a  current  made  by  this  instrument  are  very 
accurate,  when  properly  made,  and  they  are  used  as  pri- 
mary standards  in  checking  up  the  indications  of  other  cur- 
rent-measuring instruments. 

The  voltameter  is  not  suitable  for  pressure  measurements, 
since  its  resistance  is  not  constant  and,  as  a  result,  the  cur- 
rent through  it  would  not  always  be  proportional  to  the  pres- 
sure impressed  upon  the  circuit  of  which  it  is  a  part. 
Voltameters  can  not  be  used  in  the  measurement  of  an  alter- 
nating current,  since  there  would  be  a  reversal  of  chemical 
action  each  time  there  was  a  change  in  the  direction  of  the 


132  PEACTICAL  APPLIED  ELECTRICITY 

current.  If  the  same  quantity  passed  through  the  voltameter 
in  one  direction  as  passed  through  it  in  the  other,  there 
would  be  no  metallic  deposit  on  either  electrode. 

Instruments  Whose  Operation  Depends  Upon  Magnetic  Effect 
of  a  Current 

140.  Magnetic    Effect   of  a   Current. — The   magnetic   effect 
of  a  current  was  discussed  in  detail  in  the  chapter  on  "Electro- 
magnetism"   and   it   is   only   necessary  to  bear  in  mind  the 
following  facts: 

(a)  There  is  a  magnetic  field  about  a  conductor  in  which 
there  is  a  current. 

(b)  The  direction  of  the  magnetic  field  will  depend  upon 
the  direction  of  the  current  in  the  conductor. 

(c)  The  strength  or  intensity  of  this  field  will  vary  with 
the  value  of  the  current  in  the  conductor  and  the  distance 
from  the  conductor. 

Instruments  whose  operation  depends  upon  the  magnetic 
effects  of  a  current  in  a  conductor  may  be  classified  as 
follows : 

A.  Those   in    which    permanent    magnets    are    used,    they 
being  acted  upon  by  the  magnetic  field  produced  by  the  cur- 
rent.    Either  the  magnet  or  the  conductor  carrying  the  cur- 
rent may  form  the  moving  part. 

B.  Those  having  soft  iron  parts  which  are  moved  due  to 
the    magnetic    effect   produced   by    the    current   in    the    con- 
ductor. 

C.  Those  in  which  no  iron  is  used,  but  having  two  coils, 
one  of  which  is  movable.     This  coil  is  moved  due  to  a  mag- 
netic   force   that    is    exerted    between    them    when    there    is 
a   current   in   both   coils. 

CLASS  "A" 

141.  Tangent    Galvanometer   or   Ammeter. — If  a   magnetic 
needle  be  supported  in  the  center  of  a  coil  of  wire,  as  shown 
in  Fig.  96,  there  will  be  a  force  tending  to  turn  the  needle 
from  its  position  of  rest  in  the  earth's  magnetic  field  when 
there  is  a  current  in  the  coil.     This  force  will  increase  with 
an  increase  in  current  in  the  coil  and,  as  a  result,  the  needle 


ELECTRICAL  INSTRUMENTS  133 

will  be  deflected  more  and  more  as  the  current  is  increased 
until  it  occupies  a  position  that  is  almost  at  right  angles 
to  its  initial  position.  If  a  suitable  scale  be  mounted,  as 
shown  in  the  figure,  so  that  the  ends  of  the  needle,  or  a 
pointer  that  is  fastened  to  the  needle,  will  move  over  the 
scale,  the  deflection  of  the  needle  from  the  position  of  rest, 
due  to  a  certain  current,  can  be  determined. 

The  force  which  tends  to  return 
the  needle  to  its  initial  position  is 
due  to  the  magnetic  field  of  the 
earth.  In  using  the  instrument,  the 
coil  carrying  the  current  should  be 
placed  with  its  plane  parallel  to  the 
plane  of  the  needle  and  allowed  to 
remain  in  this  position  while  all  the 
readings  are  being  taken.  Such  an 
instrument  is  usually  called  a  tan- 
gent galvanometer,  or  ammeter, 
because  the  value  of  the  current  Fig.  96 

through  the  coil  is  equal  to  some 

constant  times  the  tangent  of  the  angle  through  which  the 
needle  moves.  The  indications  of  an  instrument  of  this  kind 
are  disturbed  by  the  presence  of  magnetic  fields  other  than 
that  of  the  earth,  or  the  current  in  the  coil  of  the  instrument 
itself,  and  as  a  result  its  operation  is  not  very  saisfactory 
except  under  ideal  conditions. 

142.  D'Arsonval  Instrument. — In  the  D'Arsonval  type  of 
instrument,  the  permanent  magnet  is  the  stationary  portion 
and  the  conductor  carrying  the  current  forms  the  movable 
part  of  the  instrument.  The  instrument  is  named  after  a 
French  scientist,  who  first  put  it  into  a  useful  form.  The 
cor.ductor  carrying  the  current  to  be  measured  is  bent  into 
the  form  of  a  coil  and  may  be  either  suspended  or  supported 
in  the  magnetic  field  of  the  permanent  magnet.  In  the  most 
sensitive  forms  of  the  instrument  the  coil  is  usually  sus- 
pended by  a  conducting  thread,  such  as  phosphor-bronze  or 
plated  quartz  fiber.  The  electricity  is  conducted  to  and 
from  the  coil  by  means  of  this  support  and  another  electrical 
connection  at  the  bottom  of  the  coil — which  may  consist  of 
a  second  fiber  of  the  same  material  as  the  upper  one — or 
it  may  be  a  very  fine  wire  coiled  into  a  spiral,  or  a  wire 


134 


PRACTICAL  APPLIED  ELECTRICITY 


may  dip  into  a  cup  of  mercury.  A  D'Arsonval  galvanometer 
is  shown  in  Fig.  97.  The  deflections  of  the  coil  are  measured 
by  means  of  a  telescope  and  suitable  scale,  together  with 
a  small  mirror  mounted  on  the  moving  system  of  the  instru- 
ment. The  image  of  the  scale  in  the  mirror  may  be  read 
by  means  of  the  telescope,  and  as  the  mirror  turns,  the  part 
of  the  scale  visible  through  the  telescope  changes. 


Fig.  97 


An  instrument  of  this  kind  can  be  constructed  so  that  it  is 
very  sensitive  and  will  respond  to  extremely  small  currents. 
It  is  not  subject  to  outside  disturbances  to  any  great  extent, 
such  as  stray  magnetic  fields,  changes  in  the  strength  of  the 
earth's  magnetic  field,  etc.  This  instrument  can  be  con- 
structed and  adjusted  so  that  it  may  be  used  in  measuring 
either  current  or  pressure. 

143.  D'Arsonval  Ammeters  and  Voltmeters. — The  Weston 
ammeter  and  voltmeter  are  both  good  examples  of  D'Arson- 
val instruments.  The  moving  coil  in  these  instruments  is 
mounted  on  pointed  pivots  that  are  extremely  hard  and 
rest  in  agate  jewels,  which  results  in  a  very  small  frictional 
resistance  to  the  movement  of  the  coil.  A  light  pointer  is 
attached  to  the  coil  and  so  arranged  that  it  moves  over  a 
suitable  scale  properly  graduated  and  lettered  so  that  the 
indication  of  the  instrument  may  be  easily  determined.  A 
sectional  view  of  the  moving  system  of  a  Weston  instrument 


ELECTBICAL  INSTEUMENTS 


135 


is  shown  in  Fig.  98,  with  a  portion  of  the  instrument  cut 
away  so  as  to  show  the  construction.  The  permanent  magnet 
is  of  the  horseshoe  type  and  has  two  pole  pieces  fastened 
to  its  ends  by  means  of  heavy  screws.  The  inner  surface 
of  each  of  these  pole  pieces  is  cut  so  it  forms  an  arc,  the  cen- 
ter of  which  is  midway  between  the  two  inner  surfaces  of  the 
magnet.  A  soft  iron  cylinder  is  mounted  between  the  two 
pole  pieces  and  serves  to  improve  the  magnetic  circuit.  This 


Fig.  98 


cylinder  is  mounted  on  a  piece  of  brass  that  is  fastened  to 
the  two  pole  pieces,  as  shown  in  the  figure,  there  being  a 
small  gap  between  the  cylinder  and  the  pole  pieces.  The 
coil  is  mounted  so  that  it  can  turn  about  the  cylinder.  The 
force  tending  to  return  the  coil  to  its  zero  position  is  sup- 
plied by  two  springs.  These  springs  are  so  arranged  that 
one  winds  up  when  the  other  unwinds,  due  to  a  movement 
of  the  coil.  The  electrical  connection  to  the  coil  is  made 
through  these  two  springs. 

Practically  the  same  moving  system  is  employed  in  the 
construction  of  ammeters  and  voltmeters.  In  the  ammeter,  a 
low  resistance,  capable  of  carrying  the  current  the  instru- 
ment is  supposed  to  measure,  is  connected  between  the  bind- 
ing post  on  the  instrument  case;  and  the  moving  system  is 


136 


PRACTICAL  APPLIED  ELECTEICITY 


connected  in  parallel  with  this  resistance.  Binding  posts 
are  provided  of  ample  size  to  carry  the  current.  A  We&tori 
portable  ammeter  is  shown  in  Fig.  99. 

In  the  voltmeter,  a  re- 
sistance coil  is  con- 
nected in  series  with 
the  moving  system  be- 
tween the  terminals  of 
the  instrument.  The 
value  of  the  resistance 
to  be  placed  in  series 
with  a  moving  system 
will  depend  upon  the 
voltage  a  full  scale 
reading  of  the  instru- 
ment indicates.  The 
range  of  any  voltmeter 
may  be  increased  by 

connecting  additional  resistances  in  series  with  it.  Thus,  if  a 
resistance  equal  to  that  of  the  voltmeter  itself  be  connected 
in  series  with  the  instrument,  the  voltmeter  will  indicate  only 
half  the  pressure  between  the  two  points  to  which  the 


Fig.  09 


100 


terminals  of  the  combination  are  connected.  Resistances, 
called  multipliers,  can  be  obtained  from  companies  manufac- 
turing instruments  to  be  used  in  increasing  the  range  of  a 
voltmeter. 

A  contact  key  is  usually  mounted  on  each  voltmeter  case 
and  so  arranged  that  the  circuit  of  the  instrument  may  be 
opened  or  closed  by  manipulating  the  key.  The  instrument 


ELECTRICAL  INSTRUMENTS 


137 


can  be  made  so  that  a  maximum  scale  deflection  will  cor- 
respond to  one  or  more  voltages.  Thus  an  instrument  may 
be  constructed  so  that  one  connection  will  measure  (0-3) 
volts  and  another  will  measure  (0-150)  volts.  The  resist- 
ance of  these  two  circuits  should  be  in  the  ratio  of  3  to 
150.  A  Weston  portable  voltmeter  is  shown  in  Fig.  100. 

Instruments  of  the  D'Arsonval  type  are  suitable  for  gen- 
eral use  because  they  are  "dead-beat";  that  is,  the  coil  or 
moving  system  goes  immediately  to  its  proper  position  with- 
out swinging  back  and  forth,  as  in  many  of  the  other  types. 

144.  Adaptability  of  Instruments  with  Permanent  Mag- 
nets.— Instruments  whose  operation  depends  upon  a  perma- 
nent magnet  can  be  used  only  in  direct-current  measure- 
ments, because  the  direction  of  the  deflections  is  dependent 
upon  the  direction  of  the  current  through  them. 


CLASS  "B" 

145.  Plunger  Type  Ammeter  or  Voltmeter. — The  construc- 
tion of  a  plunger  type  ammeter  or  voltmeter  is  shown  in 
Fig.  101.  The  coil  (C)  carries  the  current  to  be  measured. 
There  will  be  a  magnetic  force  exerted  on  the  rod  of  iron 
(R),  when  there  is  a  current  in  the  coil  (C),  which  will  tend 


T, 


prmg 
Vane 
Co  1 1  CO 


Fig.   101 


Fig.  102 


to  draw  the  rod  into  the  coil,  and  thus  cause  the  pointer 
(P)  to  move  over  the  graduated  scale  (S).  Gravity  is  the 
controlling  force  against  which  the  magnetic  force  of  the  coil 
acts.  The  rod  (R)  and  the  coil  (C)  are  both  formed  to  the 
same  curvature.  The  rod  (R)  is  composed  of  very  soft  iron 
and  it  becomes  a  magnet  due  to  the  action  of  the  current 


138  PRACTICAL  APPLIED  ELECTRICITY 

in  the  coil  and,  as  a  result,  is  drawn  inside  the  coil.  The 
distance  the  rod  moves  will  depend  upon  the  value  of  the 
controlling  force  and  the  ampere  turns  on  the  coil  at  any 
instant.  In  an  ammeter,  the  coil  (C)  is  wound  with  a  few 
turns  of  large  wire,  while  in  a  voltmeter  it  is  wound  with  a 
large  number  of  turns  of  small  wire,  the  ampere-turns  pro- 
ducing a  given  deflection  in  the  two  cases  being  the  same. 

146.  Magnetic  Vane  Ammeter  or  Voltmeter. — Instruments 
of  this  type  operate  on  the  principle  that  a  piece  of  soft  iron 
placed   in   a   magnetic   field   and   free   to   move   will   always 
move  into  such  a  position  that  it  will  conduct  the  maximum 
number  of  lines  of  force,   or  it  will  tend  to  move  into  the 
strongest  part  of  the  field  and  parallel  to  the  field.     Fig.  102 
shows  a  diagram  of  an  instrument  of  this  kind.    The  current 
to  be  measured  is  passed  around  the  coil   (C)    producing  a 
magnetic  field  through  the  center  of  the  coil.    A  small  piece 
of  soft  iron  called  the  vane  is  mounted  on  a  shaft  that  is 
supported  in  jewel  bearings.     This  shaft  is  not  in  the  exact 
center  of  the  coil  so  that  the  distance  the  vane  is  from  the 
inner  edge   of  the   coil   will  change   as   it  moves   about  the 
shaft.     The  magnetic  field  inside  the  coil  is  strongest  near 
the  inner  edge  and,  as  a  result,  the  vane  will  move  so  that 
the  distance  between  it  and  the  inner  edge  of  the  coil  would 
be  as  small  as  possible,  if  it  were  not  for  a  restoring  force 
supplied   by    a   coiled    spring.      The    tendency    of    this    vane 
to  rotate   increases   with  the  current  in -the  coil   and,  as  a 
result,    the    pointer   attached   to   the   moving    system   moves 
over  the  scale  with  an  increase  in  current. 

In  some  types  of  instruments  there  is  both  a  stationary  and 
a  movable  vane.  They  both  become  magnetized  to  the  same 
polarity  and,  as  a  result,  repel  each  other.  This  force  causes 
the  moving  system  to  be  deflected.  Ammeters  and  volt- 
meters operating  on  this  principle  differ  only  in  the  size 
of  wire  and  the  number  of  turns  in  the  coil  (C). 

147.  Thomson     Inclined-Coil     Instruments. — The     construe- 
tion  of  a  Thomson  instrument  is  shown  in  Fig.  103.     The  coil 
(C)    carrying   the    current   is   mounted   at   an   angle   to   the 
shaft   (S)   supporting  the  pointer   (P).     A  strip  or  bundle  of 
strips  of  iron  (I)  are  mounted  on  the  shaft  (S)  and  held  by 
a  spring,  when  there  is  no  current  in  the  coil,  so  that  its  posi- 
tion is  nearly  parallel  to  the  plane  of  the  coil.     When  a  cur- 


ELECTEICAL  INSTRUMENTS 


139 


rent  is  passed  through  the  coil,  the  iron  tends  to  take  up  a 
position  with  its  longest  dimension  parallel  to  the  magnetic 
field,  which  results  in  the  shaft  being  rotated  and  the  pointer 
moved  over  the  scale.  The  degree  of  this  movement  will 
depend  upon  the  value  of  the  current  in  the  coil. 

148.  Adaptability  of  Instruments  with  Soft  Iron  Parts. — 
The  instruments  described  in  the  previous  three  sections  may 
be  used  in  measuring  either  direct  or  alternating  currents  and 
pressures;.  Their  indications,  however,  are  not  reliable  when 
used  in  direct-current  work  because  they  are  influenced  by 
outside  fields  and  masses  of  iron.  There  is  also  a  lag  of  the 
magnetic  condition  of  the  piece  of  soft  iron  behind  the  mag- 
netizing force,  which  results  in  their  indications  being  lower 
than  the  true  value  as  the  current  is  increasing,  and  higher 


P       Spring 


Scale 


Fig.  103 

as  the  current  is  decreasing.  With  alternating  currents, 
these  objections  are  not  present  and  the  operation  of  the 
instruments  will  be  found  to  be  quite  satisfactory,  provided 
the  outside  field  does  not  change  at  the  same  frequency  as 
the  current  to  be  measured. 


CLASS  "C" 

149.  Electrodynamometer. — The  electrodynamometer  is,  per- 
haps, the  best  example  of  an  instrument  whose  operation 
depends  upon  the  magnetic  force  exerted  between  two  coils, 
both  of  which  have  a  current  in  them.  The  two  coils  are 
usually  placed  at  right  angles  to  each  other,  as  shown  in 
Fig.  104,  one  of  them  being  fastened  rigidly  to  the  frame  of 
the  instrument,  while  the  other  is  supported  or  suspended  and 
its  position  controlled  by  a  spring.  When  a  current  exists  in 


140 


PEACTICAL  APPLIED  ELECTRICITY 


both  coils,  the  movable  one  tends  to  turn  into  such  a  position 
that  its  magnetic  field  is  parallel  to  the  magnetic  field  pro- 
duced by  the  current  in  the  stationary  coil.  This  movable 
coil,  however,  is  brought  back  to  its  zero  position  by  turning 
the  thumb  screw,  which  is  connected  to  the  upper  end  of  the 
spring,  causing  the  spring  to  be  twisted  in  the  opposite  direc- 
tion to  that  in  which  the  coil  tends  to  move.  The  tortion  in 
the  spring  exactly  balances  the  tendency  for  the  coil  to  turn 
when  the  thumb  screw  has  been  turned  through  the  proper 


Fig.  104 

angle.  A  pointer  is  fastened  to  this  thumb  screw  and  moves 
over  a  graduated  scale.  The  effect  produced  by  a  given  cur- 
rent through  the  two  coils,  which  are  connected  in  series,  is 
then  read  as  so  many  divisions  on  the  scale. 

When  the  instrument  is  used  as  an  ammeter,  the  two  coils 
consist  of  a  few  turns  of  large  wire,  depending,  of  course, 
on  the  current  capacity  of  the  instrument.  Quite  often  the 
stationary  coil  is  divided  into  two  parts,  only  part  of  the 
turns  being  used  in  series  with  the  movable  coil  for  one 


ELECTKICAL  INSTRUMENTS  141 

connection,  while  all  the  turns  may  be  used  if  desired.  The 
current  required  to  produce  a  full  scale  deflection  when 
all  the  turns  in  the  stationary  coil  are  in  use  will  be  less 
than  the  current  required  when  only  a  portion  of  the  turns 
are  used. 

When  the  instrument  is  used  as  a  voltmeter,  the  coils  are 
composed  of  a  large  number  of  turns  of  small  wire.  Often  an 
additional  resistance  is  provided  to  be  used  in  series  with  the 
instrument,  which  increases  its  range  as  a  voltmeter. 

150.  Adaptability. — The  indications  of  instruments  of  the 
electrodynamometer  type  are   influenced   by   stray   magnetic 
fields  and,  as  a  result,  they  are  not  altogether  satisfactory 
for  direct-current  measurements.     This  error,   however,  can 
be  reduced  to  practically  zero,  if  the  disturbing  effect  remains 
constant — which   is  not  very  often  the   case — by  taking  the 
average  of  two  readings  of  the  instrument  with  the  current 
through  it  in  opposite  directions  in  the  two  cases.    The  above 
errors   do   not  occur   when   instruments   of   the   electrodyna- 
mometer type  are  used  in  alternating-current  measurements 
— unless  frequency  of  the  distributing  field  is  the  same  as  the 
frequency  of  the  current  in  the  instrument — as  the   current 
is  continuously  reversing  in  direction. 

Instruments  Whose  Operation   Depends   Upon    Heating   Effect 
of  a  Current 

151.  Heat  Generated    in   a  Conductor  Carrying  a  Current. 
— When   there    is    a    current   produced    in    a    conductor,    the 
energy  expended  in  overcoming  the  conductor's  resistance  is 
manifested  in  the  form  of  heat.    Dr.  Joule  discovered  that  the 
heat  developed  in  a  conductor  carrying  a  current  was  pro- 
portional to 

(a)  The  resistance  of  the  conductor. 

(b)  The  square  of  the  current  in  the  conductor. 

(c)  The  time  the  current  exists  in  the  conductor. 

He  also  determined  by  experiment  that  778  foot-pounds 
of  work  would  raise  the  temperature  of  1  pound  of  water 
1°  Fahrenheit.  This  quantity,  778  foot-pounds,  is  called  the 
mechanical  equivalent  of  heat,  or  Joule's  equivalent.  A  pound 
of  water  can  be  heated  electrically  by  immersing  a  conductor 
carrying  a  current  in  the  water  until  its  temperature  is  raised 


142  PRACTICAL  APPLIED  ELECTRICITY 

1°  Fahrenheit,  or  the  same  work  will  be  done  electrically 
as  was  previously  done  mechanically.  Joule  found  by  experi- 
ment that  1  ampere  under  a  pressure  of  1  volt  in  a  circuit  for 
1  second,  or  1  watt  expended,  would  do  the  same  work  as 
'0.7373  foot-pound  expended  in  1  second,  or 

1  watt  =  0.7373  foot-pound  per  second  (88) 

The  British  thermal  heat  unit  (abbreviated  b.t.u.)  is  de- 
fined as  the  amount  of  heat  required  to  raise  one  pound  o£ 
water  1°  Fahrenheit  at  its  maximum  density  (39.1°  Fahren- 
heit). Since  778  foot-pounds  of  work  is  equivalent  to  1 
b.t.u.  and  1  watt  is  equal  to  .7373  foot-pound  per  second,  then 
1  watt  acting  for  1  second  will  develop  .000  947  7  b.t.u.,  or 

b.tu.  =  .000  947  7  X  (E  X  I)  X  t  (89) 

Substituting  for  (E)  its  value,  (I  X  R),  gives 
b.tu.  =  .000  947  7  X  I2R  X  t 

Example. — What  current  must  be  passed  through  a  resist- 
ance of  100  ohms  immersed  in  10  pounds  of  water  in  order 
that  its  temperature  be  raised  80°  Fahrenheit  in  5  minutes? 

Note:  (All  losses  due  to  radiation  are  to  be  neglected  and 
all  the  energy  is  supposed  to  be  converted  into  heat). 

Solution. — There  will  be  80  b.t.u.  required  for  each  pound 
of  water  or  a  total  of  80x10  =  800  b.t.u.  Substituting  in 
equation  (89)  gives 

800  =  .000  947  7  X  12  X  100  X  (5  X  60) 
800  8 

12  =  _ 

.0009477X100X300         .28431 

12  =  28.13 
I   ='5.3+ 

Ans.     5.3-f-  amperes. 

152.  Commercial  Applications  of  the  Heating  Effect  of  a 
Current. — Numerous  practical  applications  are  made  of  the 
heating  effect  of  a  current  in  a  conductor,  such  as  electric 
irons,  cooking  stoves,  heaters,  lamps,  electric  welding,  fuses, 
etc.  Since  the  heat  generated  in  any  part  of  a  circuit  is 
proportional  to  the  resistance  of  the  part  considered,  it  fol- 
lows that  it  is  always  desirable  to  have  all  conductors  used 


ELECTKICAL  INSTRUMENTS  143 

in  transmitting  electrical  energy  of  as  low  resistance  as  pos- 
sible in  order  that  the  loss  in  transmission  be  a  minimum. 
On  the  other  hand,  when  it  is  desired  to  generate  heat,  resist- 
ance is  introduced  and  the  value  of  the  heat  generated  can  be 
determined  by  the  use  of  equation  (89).  If  none  of  the 
heat  generated  in  a  circuit  were  carried  away,  the  temperature 
of  the  conductor  would  continue  to  rise  as  long  as  there 
was  a  current  in  it.  As  a  matter  of  fact,  however,  the  tem- 
perature of  a  conductor  will  rise  until  the  heat  radiated  is 
exactly  equal  to  the  heat  generated  in  a  given  time.  This 
rise  in  temperature  may  be  excessive  and  for  that  reason 
the  Fire  Underwriters  limit  the  value  of  the  current  a  con- 
ductor should  carry.  Table  G,  in  Chapter  20,  gives  the  cur- 
rent-carrying capacity  of  different  sized  wires.  These 
values  may  be  exceeded  without  any  injurious  effect,  but 
it  is  always  essential  to  keep  within  the  values  allowed  by 
the  Underwriters  as  the  likelihood  of  a  fire  due  to  an  over- 
heated or  burnt-out  circuit  is  less  than  it  would  be  if  the 
circuit  were  overloaded.  The  size  of  the  conductor  used  in 
electrical  heating  utensils  is  just  sufficient  to  carry  the 
current  without  being  injured. 

In  electric  welding  a  large  current  is  passed  between  the 
surfaces  that  it  is  desired  to  weld  together  and  the  heat 
generated  is  sufficient  to  raise  the  materials  to  a  welding 
temperature.  The  heat  generated  in  an  incandescent  lamp 
raises  the  temperature  of  the  filament  to  such  a  value  that 
it  will  emit  light. 

The  electric  fuse  is  a  device  whose  function  is  to  auto- 
matically open  a  circuit  in  which  there  is  an  excessive  cur- 
rent. The  fuse  usually  consists  of  a  material  that  will  melt 
at  a  much  lower  temperature  than  the  material  compos- 
ing the  remainder  of  the  circuit.  It  is  nothing  more  than 
a  weak  spot  in  the  circuit  which  is  capable  of  conducting 
the  current  the  circuit  is  supposed  to  carry,  but  will  melt 
when  the  current  through  it  becomes  excessive.  The  val- 
ues of  the  current  required  to  fuse  different  sizes  of  wires 
is  given  in  Table  H,  in  Chapter  20. 

153.  Hot-Wire  Instruments.— The  heat  generated  in  a  con- 
ductor due  to  a  current  in  it  will  cause  the  conductor  to 
expand.  The  amount  of  this  expansion  will  depend  upon 
the  rise  in  temperature,  which,  in  turn,  depends  upon  the  cur- 


144 


PEACTICAL  APPLIED  ELECTRICITY 


rent  in  the  conductor.  The  principle  on  which  hot- 
wire instruments  operate  is  shown  diagrammatically 
in  Fig.  105.  A  wire  (AB)  of  comparatively  high  re- 
sistance, low  temperature  coefficient,  and  non-oxidizable 
metal,  has  one  end  attached  to  the  plate  (C),  then  passed 
around  a  pulley  (P)  that  is  secured  to  a  shaft  (S),  and  its  free 
end  is  brought  back  and  mechanically,  though  not  electrically, 
attached  to  the  plate  (C).  The  spring  (F)  keeps  the  wire 
under  tension,  it  being  attached  to  the  plate  (C),  which  is 
so  guided  that  it  can  move  in  a  direction  at  right  angles  to 
the  shaft  (S).  An  arm  (G)  is  also 
attached  to  the  shaft  (S),  it  being  coun- 
terweighted  at  the  upper  end  and  bifur- 
cated at  the  lower  end.  A  fine  silk  thread 
(T)  has  ore  end  attached  to  one  of  the 
arms  of  (G),  then  passed  around  a  small 
pulley  (H),  which  is  mounted  on  a  shaft 
that  carries  a  pointer  (I),  and  finally  has 
its  other  end  attached  to  the  second  arm 
of  (G).  The  material  composing  the  arms 
of  (G)  is  springy  and  serves  to  keep 
the  silk  fiber  in  tension.  The  current 
to  be  measured  passes  through  the  wire 
(A),  entering  and  leaving  through  two 
twisted  conductors,  as  shown  in  the 
figure.  When  a  current  is  passed  through 
(A)  it  is  heated  and  expands,  which 
results  in  the  tension  in  (A)  being 

less  than  that  in  (B) — they  were  originally  the  same — and 
equilibrium  can  be  restored  only  by  the  pulley  (P)  rotating 
in  a  clockwise  direction.  This  rotation  of  the  pulley  (P) 
causes  the  lower  end  of  the  arm  (G)  to  move  toward  the  left, 
and  the  silk  thread  that  passes  around  the  pulley  (H)  causes 
it  to  rotate  in  a  clockwise  direction  and,  as  a  result,  the 
pointer  (I)  is  deflected  to  the  right,  it  being  rigidly  attached 
to  the  pulley  (H).  The  operation  of  this  instrument  is 
quite  satisfactory,  as  any  change  in  the  temperature  of  the 
room  in  which  it  is  used  does  not  affect  the  correctness  of 
its  indications,  since  both  parts  of  the  wire  (AB)  are  af- 
fected to  the  same  extent,  which  results  in  no  movement  of 
the  pointer.  In  a  great  many  instruments  no  adjustment  or 


ELECTEICAL  INSTBUMENTS  145 

compensation  is  provided  for  errors  due  to  changes  in  room 
temperatures.  In  the  case  of  ammeters,  a  low-resistance  in- 
strument is  usually  used  in  parallel  with  a  suitable  shunt, 
while  in  the  case  of  voltmeters  a  high  resistance  instrument 
is  employed. 

154.  Adaptability  of  Hot-Wire  Instruments. — Hot-wire  in- 
struments may  be  used  equally  well  in  both  alternating  and 
direct-current  measurements,  the  heating  effect  of  the  cur- 
rent being  independent  of  its  direction. 


Instruments    Whose    Operation     Depends    Upon    the    Electro- 
static Effect 

155.  Condenser. — Two  conductors  separated  by  an  insu- 
lator, which  is  called  the  dielectric,  constitute  what  is  called 
a  condenser.  When  the  terminals  of  a  condenser  are  con- 
nected to  some  source  of  electrical  energy,  such  as  a  bat- 
tery or  a  dynamo,  there  will  be  a  certain  quantity  of  elec- 
tricity stored  in  the  condenser.  The  value  of  the  quantity 


Plates        Dielectric 


Fig.  106  Fig.   107 

stored  will  depend  upon  the  capacity  of  the  condenser  and 
the  electrical  pressure  to  which  its  terminals  are  subjected. 
A  condenser  is  said  to  have  a  capacity  equal  to  unity,  or  1 
farad,  when  a  unit  of  quantity,  1  coulomb,  will  produce 
a  difference  in  pressure  between  its  terminals  of  1  volt. 
A  simple  form  of  condenser  is  shown  in  Fig.  106,  which  con- 
sists of  two  metallic  plates  separated  by  a  sheet  of  paraf- 
fine  paper.  The  capacity  of  such  a  condenser  will  depend 
upon  the  area  of  the  plates  used  in  the  construction,  the 
number  of  plates,  the  distance  between  the  plates,  or  the 
thickness  of  the  dielectric,  and  the  kind  of  material  com- 
posing the  dielectric.  The  value  of  an  insulating  material 
as  a  dielectric  is  called  its  specific  indoctive  capacity.  The 


146  PEACTICAL  APPLIED  ELECTEICITY 

inductive  capacity  of  different  materials  varies  considerably, 
but  it  is  less  through  air  than  it  is  through  any  solids  or 
liquids.  As  a  result,  a  condenser  that  has  air  for  a  dielec- 
tric will  have  less  capacity  than  one  that  has  a  solid  or 
liquid  dielectric,  the  dimensions  of  the  condensers  being 
the  same.  The  specific  inductive  capacity  of  a  material  is 
measured  in  terms  of  air  as  a  standard,  and  it  is  the  ratio 
of  the  capacities  of  two  condensers,  one  of  which  has  the 
material,  whose  dielectric  constant  is  to  be  determined,  as 
a  dielectric,  and  the  other  has  air  as  a  dielectric.  The  di- 
mensions of  the  two  condensers  must  be  the  same.  Table 
No.  VIII  gives  the  value  of  the  specific  inductive  capacity  of 
some  of  the  materials  that  are  commonly  used  in  the  con- 
struction of  condensers. 


TABLE  NO.  VIII 

SPECIFIC  INDUCTIVE  CAPACITIES 

Specific 
Inductive 
Capacity 
4.38 
2.52 
2.30 
3.35 

2.50  to  3.80 
2.20 
2.17 

Condensers  used  in  practice  usually  consist  of  more  than 
two  plates,  as  shown  in  Fig.  106.  An  arrangement  similar 
to  that  shown  in  Fig.  107  is  usually  used  where  alternate 
plates  are  connected  together  and  form  one  terminal,  while 
the  remaining  plates  are  connected  together  and  form  the 
other  terminal.  The  capacity  in  farads  of  such  a  combina- 
tion of  plates  as  that  shown  in  B'ig.  107  can  be  calculated 
by  the  use  of  the  equation 

K  (n  — 1)  a 

C  = (90) 

4.452  X  1012  x  d 

where  (n)  represents  the  total  number  of  plates  used  in  the 
construction  of  the  condenser,  (K)  represents  the  constant  of 
the  dielectric,  (a)  represents  the  area  of  each  plate  in  square 
inches,  and  (d)  is  the  distance  between  the  plates  in  inches. 


Material 

Air 
Alcohol   (Amyl) 
Glass   (Plate) 
Gutta-percha 
Mica 
Parafflue 
Petroleum 

Specific 
Inductive 
Capacity 
1.00 
15.50 
3.00  to  7.00 
2.50 
6.70 
1.90  to  2.40 
2.10 

Material 

Porcelain 
Resin 
Rubber 
Shellac 
Sulphur 
Turpentine 
Vaseline 

ELECTEICAL  INSTRUMENTS 


147 


Example. — Determine  the  capacity  of  a  condenser  of  100 
sheets  of  tinfoil  10  X  10  inches,  that  are  separated  by  plate 
glass  whose  dielectric  constant  is  5.  and  0.1  of  an  inch  in 
thickness. 

Solution. — Substituting  the  values  of  the  above  quantities 
in  equation  (90)  gives 

5  X  (100-1)  X  10  X  10 

C  (in  farads)  =  =  .000  000  111  2 

4.452  X  1012  X  0.1 

Ans.     .000  000  111  2  farads. 

The  farad  is  a  unit  of  capacity  entirely  too  large  for  prac- 
tical use  so  a  smaller  unit,  or  the  microfarad,  is  used.  The 
microfarad  is  equal  to  one-millionth  of  a  farad. 


Fig.  108 


Fig.  109 


156.  Connection  of  Condensers  in  Series  and  Parallel.— 
Condensers  may  be  connected  in  series  or  in  parallel,  or  in  any 
combination  of  series  and  parallel,  just  as  resistances.  The 
capacity  of  a  combination  of  condensers  may  be  calculated 
by  the  use  of  one  of  the  following  equations.  When  a  num- 
ber of  condensers  are  connected  in  series,  as  shown  in  Fig. 
108,  the  total  capacity  (C)  of  the  combination  will  be  given  by 
the  equation 


1111 

-H h--  +  etc. 

C      G        C        C 


(91) 


This  results  in  the  combined  capacity  of  several  condensers 
in  series  being  less  than  the  capacity  of  any  one  of  them. 


148  PRACTICAL  APPLIED  ELECTRICITY 

If  there  are  only  two  connected  in  series,  the  combined  ca- 
pacity will  be  equal  to 

CiC2 
C  =  --  (92) 


It  is  seen  that  the  above  equation  is  similar  to  the  one  used 
in  calculating  the  combined  resistance  of  a  number  of  re- 
sistances in  parallel. 

When  a  number  of  condensers  are  connected  in  parallel, 
as  shown  in  Fig.  109,  the  total  capacity  (C)  of  the  combina- 
tion will  be  equal  to 

C  =  Ci  +  C2  +  C3  +  etc.  (93) 

The  combined  capacity  of  several  condensers  in  parallel 
will  be  greater  than  the  capacity  of  any  single  condenser. 
This  equation  is  similar  to  the  one  used  in  calculating  the 
combined  resistance  of  several  resistances  in  series. 

157.  Relation  of  Impressed  Voltage,  Quantity,  and  Con- 
denser Capacity.  —  If  a  condenser  is  said  to  have  unit  capacity 
•when  1  coulomb  of  electricity  will  produce  a  difference 
in  electrical  pressure  between  its  terminals  of  1  volt,  then 
1-volt  pressure  applied  at  the  terminals  will  produce  a  charge 
of  unit  quantity,  1  coulomb,  if  the  capacity  is  1  farad.  If 
1-volt  pressure  produces  a  charge  of  2  coulombs,  the  capacity 
is  2  farads;  or  if  1-volt  pressure  produces  a  charge  of  one-half 
coulomb,  the  capacity  is  one-half  farad.  If  the  capacity  of  a 
condenser  is  constant,  the  quantity  of  charge  is  directly  pro- 
portional to  the  impressed  voltage;  or  if  the  impressed  voltage 
is  constant,  the  quantity  of  charge  is  directly  proportional 
to  the  capacity.  These  two  statements  may  be  combined  in 
an  equation  which  states  that  the  quantity  varies  directly  as 
the  capacity  and  the  impressed  voltage,  or 

Q  =  CE  (94) 

The  above  equation  gives  the  value  of  the  quantity  in  cou- 
lombs stored  in  a  condenser  whose  capacity  is  (C)  farads, 
when  it  is  subjected  to  a  pressure  of  (E)  volts.  Since  the 
microfarad  is  the  more  common  unit  of  capacity,  it  being 
equal  to  the  one-millionth  part  of  a  farad,  the  above  equa- 


ELECTEICAL  INSTRUMENTS  149 

tion  may  be  rewritten  with  the  value  of  (C)  m  microfarads, 
which  gives 

Cn,f. 
Q  = E  (95) 

106 

It  is  often  desirable  to  measure  the  quantity  in  a  unit  smaller 
than  the  coulomb,  in  which  case  the  microcoulomb  is  used, 
it  being  the  one-millionth  part  of  a  coulomb. 


PROBLEMS   OF   CONDENSERS 

(1)  Calculate  the  capacity  of  a  telephone  condenser  com- 
posed   of  1001    sheets   of   tinfoil   3X6   inches,   separated   by 
paramne  paper  .007  of  an  inch  thick,  and  having  a  dielectric 
constant  of  2. 

Ans.     1.15  -f  microfarads. 

(2)  Two  condensers  of  4  and  6  microfarads,  respectively, 
are  connected  in  series.    Calculate  their  combined  capacity. 

Ans.     2.4  microfarads. 

(3)  What  quantity  of  electricity  will  be  stored  in  the  two 
condensers  in  problem  2  when  they  are  connected  in  series 
and  there  is  an  electrical  pressure  of   100  volts   applied   to 
the  terminals? 

Ans.    .000  24  coulomb,  or  240  microcoulombs. 

(4)  Two  condensers  of  4  and  6  microfarads,  respectively, 
are  connected  in  parallel.     Calculate  their  combined  capacity. 

Ans.     10  microfarads. 

(5)  What   quantity   in   microcoulombs   will    be    stored    in 
each   condenser   when   there   is   a  pressure   of   100   volts   ap- 
plied to  the  terminals  of  the  combination  in  problem  4? 

Ans.      400    microcoulombs    in    4    m.f.    condenser;    600    micro- 
coulombs  in  6  m.f.  condenser. 

(6)  What  pressure   is   required   to   charge  a  2-microfarad 
condenser  with  a  charge  of  .0002  coulomb? 

Ans.     100  volts. 

(7)  What  is  the  capacity  of  a  condenser  when  100  volts 
will  give  it  a  charge  of  .00015  coulomb? 

Ans.     1.5  microfarads. 


150 


PEACTJCAL  APPLIED  ELECTKICITY 


158.  Electrostatic  Voltmeter. — The  electrostatic  voltmeter 
is  really  nothing  more  than  a  condenser  constructed  so  that 
one  plate  may  move  with  respect  to  the  other.  When  a 
condenser  is  charged,  there  is  a  force  tending  to  draw  the 
plates  together,  due  to  the  charges  of  opposite  kind  on  the 
two  sets  of  plates,  and  it  is  this  force  that  produces  the 
deflection  in  the  case  of  an  electrostatic  voltmeter.  In  some 
instruments  only  two  plates  are  used,  while  in  others  a 
number  of  plates  are  used  to  form  each  terminal,  the  con- 
struction being  such  that  the  movable  plates  move  between 
the  stationary  plates. 


Fig.  Ill 


An  electrostatic  voltmeter  suitable  for  measuring  extremely 
high  voltages  is  shown  diagrammatically  in  Fig.  110.  The 
principal  parts  are  the  moving  elements  (Mj)  and  (M2),  the  • 
curved  plates  (Bj)  and  (B2),  the  condensers  (C^)  and  (C2), 
scale  (S),  pointer  (P),  and  terminals  (Tx)  and  (T2).  The 
plate  (Bj)  is  connected  to  the  inner  plate  of  (Cj)  and  (B2) 
to  the  inner  plate  of  (C2).  The  plates  (Bx)  and  (B2)  are 
so  arranged  with  respect  to  (M^  and  (M2),  which  are  elec- 
trically connected,  that  an  angular  deflection  of  the  pointer 
over  the  scale  in  the  positive  direction  (above  zero)  short- 
ens the  gap  between  the  moving  elements  and  the  fixed 
plates.  The  charges  on  the  plates  (B^  and  (B2)  are  of  op- 
posite sign  and  they  induce  opposite  charges  on  (M.^)  and 


ELECTRICAL  INSTRUMENTS  151 

(M2),  which  results  in  a  force  that  tends  to  cause  the  mov- 
ing system  to  turn  about  its  own  axis,  or  into  such  a  posi- 
tion that  (Mj)  and  (M2)  are  nearer  (Bj.)  iind  (B2).  The 
movement,  however,  is  restrained  by  means  of  a  spiral  spring 
and  the  deflection  is  indicated  by  the  pointer  (P)  on  the 
scale  (S).  The  form  of  the  plates  (E^)  and  (B2)  is  such 
that  the  deflection  increases  almost  directly  as  the  impressed 
voltage.  The  condensers  (Cx)  and  (C2)  are  so  constructed 
that  either  or  both  of  them  may  be  short-circuited,  which 
results  in  the  pressure  required  to  produce  a  full  scale  de- 
flection being  less  than  when  they  are  in  circuit,  thus  giving 
a  wide  range  to  the  instrument.  The  moving  system  is  im- 
mersed in  a  tank  of  oil,  which  affords  a  good  insulation  and 
buoys  up  the  moving  system,  practically  removing  all  the 
weight  from  the  bearings.  Instruments  of  this  type  are  con- 
structed to  measure  voltages  up  to  200  000  volts.  An  in- 
terior view  of  the  various  parts  is  shown  in  Fig.  111.  There 
are  many  other  forms  of  electrostatic  voltmeters  on  the  mar- 
ket, but  their  operation  is  based  on  the  same  fundamental 
principle  as  the  one  just  described,, 

159.  Adaptability    of     Electrostatic    Instruments.— Electro- 
static instruments  may  be   used   in  measuring  either  direct 
or  alternating  pressures.     Their  operation   is  more  satisfac- 
tory, however,  on  an  alternating-current  circuit,  because  a.c. 
pressures  are,  as  a  rule,  larger  in  value  than  d.c.  pressures. 
Their   operation   is   not   at   all    satisfactory   when   the    pres- 
sure to  be  measured  is  below  50  volts,  and  for  this  reason 
they   cannot   be   used   in   combination   with   a   shunt   in  the 
measurement   of   currents,    as   the    resistance    of   the    shunt 
would  have  to  be  large  in  order  that  there  be  the  proper 
difference  in  pressure  between  its  terminals  to  operate  the 
meter.     A  high-resistance  shunt  of  this  kind  in  any  circuit 
would  mean  a  large  loss  in  comparison  to  that  which  would 
occur  if  a  low-resistance  shunt  could  be  used. 

Measurement   of    Electric    Power   and    Construction    of   Watt- 
meters 

160.  Measurement  of  Power. — The  power  that  is  used  in 
any  part  of  a  direct-current  circuit  may  be  determined  by 
measuring  the  current  with  an  ammeter,  and  the  difference 
in  pressure,  by  means  of  a  voltmeter,  between  the  terminals 


152 


PEACTICAL  APPLIED  ELECTRICITY 


of  the  portion  of  the  circuit  in  which  it  is  desired  to  ascer- 
tain the  power.  The  power  can  then  be  calculated  by  multi- 
plying the  ammeter  reading,  in  amperes,  by  the  voltmeter 
reading,  in  volts,  or 

W  =  IE  (96) 

Thus  the  power  taken  by  the  ten  incandescent  lamps  shown 
in  Fig.  112  can  be  determined  by  connecting  the  ammeter 
(A)  and  the  voltmeter  (V),  as  shown  in  the  figure,  and  noting 
their  indication  when  the  lamps  are  turned  on.  (All  of  the 
lamps  are  not  shown).  The  product  of  these  instrument 
readings,  in  volts  and  amperes,  will  give  the  power  in  watts. 
When  the  connections  are  made,  as  shown  in  Fig.  112,  the 


Load     I     L     I     C 


Ten  Lamps 


Fig.  112 

ammeter  indicates  the  current  through  the  lamps  and  volt- 
meter combined.  This  results  in  a  small  error  in  the  cal- 
culation of  the  power  taken  by  the  lamps,  provided  the 
current  through  the  voltmeter  is  small  in  comparison  to 
the  current  through  the  lamps.  For  very  accurate  measure- 
ments, the  current  through  the  voltmeter  should  always  be 
subtracted  from  the  total  current  indicated  by  the  ammeter. 
If  the  voltmeter  be  connected  across  the  line  before  the 
ammeter — that  is,  the  ammeter  would  be  between  the  volt- 
meter connection  and  the  lamps — the  indication  of  the  volt- 
meter would  not  be  the  true  value  of  the  pressure  between 
the  terminals  of  the  lamps,  as  there  would  be  a  certain  drop 
in  pressure  across  the  ammeter.  The  drop  across  the  amr 
meter  should  be  subtracted  from  the  voltmeter  indication 
in  order  to  obtain  the  true  pressure  across  the  lamps.  With 


ELECTRICAL  INSTRUMENTS 


153 


a  low-resistance  ammeter,  this  drop  is  very  small  and  may 
be  neglected  except  when  very  accurate  results  are  desired. 

161.  Principle  of  the  Wattmeter. — Wattmeters  are  so  con- 
structed that  their  indication  is  proportional  to  the  product 
of  a  current  and  an  electrical  pressure;  hence,  they  indicate 
the  power  direct.  Instruments  of  this  kind  are  called  watt- 
meters, because  they  measure  watts. 

The  principle  of  the  wattmeter  can  be  illustrated  by  ref- 
erence to  Fig.  113,  which  shows  an  electrodynamometer 
with  one  coil  connected  in  series  with  the  line  and  the  other 
coil  connected  across  the  line.  The  coil  connected  in  series 
with  the  line  is  wound  as  though  it  were  to  be  used  as  an 
ammeter,  and  consists  of  a  few  turns  of  large  wire,  while 
the  coil  connected  across  the  line  is  wound  as  though  it  were 
to  be  used  as  a  voltmeter  and  consists  of  many  turns  of 
fine  wire.  These  two  coils  will  be  called  the  pressure  coil  and 
the  series  coil,  respectively. 

The  actual  operation  of  such  a  meter  can  best  be  explained 
by  taking  a  practical  example  sim- 
ilar to  that  shown  in  Fig.  113.    The 
current   through  the   lamps   passes 
through    the    current    coil    of    the 
meter  and  produces  a  certain  mag- 
netic effect,  which  changes  in  value 
as    the   current   changes   in   value. 
There  will  also  be  a  magnetic  effect 
produced  by  the  current  that  exists 
in  the  pressure  coil.    The  current  in 
the    pressure    coil,    or    circuit,    will 
vary  with  the  difference  in  pressure 
between  the  terminals  of  the  circuit, 
since  the  resistance  of  the  circuit 
remains  constant  and,  as  a  result, 
the  magnetic  field  about  the  pres- 
sure coil  will  vary  with  the  voltage  of  the  line.    The  deflection 
of  the  moving  coil  of  the  electrodynamometer  is  proportional 
to  the  product  of  the  magnetic  effects  of  the  two  coils,  and  since 
the  magnetic  effects  of  the  two  coils  are  proportional  to  the 
current  and  the  voltage,  respectively,  the  indication  of  the 
instrument  must  be  proportional  to  the  product  of  (E)  and  (I), 
or  it  irdicates  watts. 


Pressure 
i/Cci, 


Fig.  113 


154 


PRACTICAL  APPLIED  ELECTRICITY 


When  an  instrument  of  this  kind  is  connected  in  a  cir- 
cuit in  which  a  fluctuating  current,  due  to  a  varying  load, 
exists,  the  pressure  between  lines  remaining  constant,  the 
indications  will  vary  directly  with  the  load  current.  The 
magnetic  effect  due  to  the  current  in  the  pressure  circuit  re- 
mains constant,  since  the  voltage  or  pressure  impressed  upon 
this  circuit  remains  constant.  When  the  load  current  re- 
mains constant  and  the  voltage  varies,  the  magnetic  effect 
of  the  current  in  the  series  coil  remains  constant  and  the 
magnetic  field  about  the  pressure  coil  changes  and  the  de- 
flection varies  with  the  voltage. 

162.  Whitney  Wattmeter. — The  principle  of  this  wattmeter 
is  the  same  as  that  of  the  dynamometer  wattmeter  just  de- 
scribed, except  that  the  construction  is  modified  to  make 

the  instrument  portable  and 
more  suitable  for  commer- 
cial work.  In  this  wattmeter 
the  heavy  current  winding 
is  composed  of  two  coils, 
which  are  supported  in 
suitable  frames  and  enclose 
a  coil  composed  of  fine  wire. 
This  coil  is  mounted  on  a 
shaft  with  pointed  ends  rest- 
ing in  jeweled  bearings. 
Two  volute  springs  serve  to 
hold  the  coil  in  its  zero  posi- 
tion and  balance  the  turning 
effort  of  the  coil  when  there 
is  a  current  in  it.  These  two 
springs  also  serve  to  con- 
duct the  electricity  into  and 

from  the  movable  coil,  instead  of  the  mercury  cups,  as  in  the 
previous  case.  A  balance  is  obtained  by  turning  the  torsion 
head  until  the  needle  that  is  attached  to  the  movable  coil  is 
indicating  no  deflection,  the  reading  of  the  pointer  attached  to 
the  torsion  head  is  then  noted  and  represents  the  indication  of 
the  instrument.  The  scale  of  the  instrument  may  be  divided 
into  degrees,  and  the  deflection  read  on  this  scale  must  be 
multiplied  by  some  constant  to  obtain  the  power  indicated  by 
the  instrument,  or  the  scale  may  be  so  drawn  that  the  power 


Fig.  114 


ELECTRICAL  INSTRUMENTS  155 

in  watts  can  be  read  directly  from  it.  The  general  appearance 
of  the  instrument  is  shown  in  Fig.  114. 

163.  Weston  Wattmeter. — The  principle  of  this  instrument 
is  practically  the  same  as  the  one  described  in  the  previous 
section.    No  torsion  head,  however,  is  used  and  the  pressure 
coil,    instead   of   being   maintained    at   practically   the    same 
position  for  all  indications  of  the  instrument,  rotates  about 
its  axis  through  an  angle  of  approximately  eighty  degrees. 
Two    volute    springs    serve    to    conduct   the    electricity    into 
and  from  the   movable   coil.     They  also  offer  the  opposing 
force  to  that  produced  by  the 

magnetic  effect  of  the  cur- 
rents in  the  two  coils.  This 
form  of  instrument  has  an  ad- 
vantage over  the  other  forms 
described  in  that  no  manipu- 
lation is  necessary  and  the 
needle  points  at  once  to  the 
scale  mark  showing  the  watts. 
A  Weston  instrument  is 
shown  in  perspective  in  Fig. 
115  and  diagrammatically  in 
Fig.  116.  In  Fig.  116  (C^  and 

(€2)  represent  the  two  current  coils,  which  are  connected  in 
series  between  the  two  posts  numbered  (1)  and  (2).  The 
pressure  connections  can  be  made  to  (3)  and  (5),  or  (3)  and 
(6).  The  resistance  between  (3)  and  (6)  is  usually  just  half 
the  value  of  the  resistance  between  (3)  and  (5). 

164.  Compensated    Wattmeter. — The    power    indicated    by 
a  wattmeter  will  be  in  error  just  the  same  as  the  value  of 
the  power  determined  by  the  voltmeter  and  ammeter  read- 
ings is  in  error,  due  to  the  current  taken  by  the  voltmeter, 
or  the  drop  across  the  ammeter,  unless  some  means  be  pro- 
vided that  will  counteract  or  compensate  for  this  error.    This 
compensation   is   provided   in   the  Weston   wattmeter   in   the 
following  way:      The  pressure   circuit  is   always  to   be   con- 
nected across  the  line  after  the  current  coil,  which  results 
in  the  current  coil  carrying  the  current  that  passes  through 
the   pressure  circuit.     This   current   in   itself  would   produce 
a  deflection,  even  though  there   be  no  load  on   the   circuit, 
and,  as  a  result,  the  meter  would  always  indicate  a  higher 


156 


PEACTICAL  APPLIED  ELECTKICITY 


-J      /— <A/WAAVWV — ' 


value  of  power  than  that  actually  taken  by  the  load.  If, 
however,  the  pressure  circuit  be  wound  around  the  series 
coil  the  same  number  of  times  there  are  turns  in  the  series 
coil,  and  this  winding  be  so  connected  that  the  magnetic 
effect  of  the  current  in  it  is  opposite  to  that  of  the  cur- 
rent in  the  series  coil,  the  magnetic  field  produced  by  the 
pressure  current  passing  through  the  series  coil  will  be 
completely  annulled  and  there  will  be  no  deflection  of  the 
moving  system  until  there  is  a  load  current  through  the 
series  coil.  The  turns  of  wire  that  are  wound  around  the 
series  coil  are  called  compensating  turns  and  they  are  shown 

in  Fig.  116.  When  a  sepa- 
rate source  of  current  and 
potential  is  used  in  cali- 
brating wattmeters,  there 
should  be  no  compensating 
turns  in  the  circuit,  and 
terminal  (4)  should  be 
used  instead  of  terminal 
(3).  The  resistance  of  the 
pressure  circuit  should  be 
the  same  in  both  cases, 
and  a  small  coil  (R),  whose 
resistance  is  equal  to  that 
of  the  compensating  turns, 
is  connected  in  the  pres- 
sure circuit  instead  of  the 
compensating  turns. 

165.       Adaptability 

of  Wattmeters. — All  wattmeters  that  have  been  described  will 
operate  on  either  direct-  or  alternating-current  circuits.  Their 
indications  on  direct-current  circuits  will,  however,  be  in- 
fluenced by  stray  magnetic  fields,  and,  in  the  majority  of  cases, 
a  reversal  of  current  through  the  coils,  although  the  current 
remains  constant  in  value,  will  result  in  a  different  indication. 
When  the  instruments  are  used  in  an  alternating-current  cir- 
cuit, these  errors  are  very  much  reduced — provided  the  dis- 
turbing field  is  not  alternating — since  the  current  passes 
through  the  circuit  in  one  direction  for  the  same  time  it  passes 
in  the  opposite  direction. 

166.     Watt-Hour  Meters.— The  Weston  wattmeter,  described 


Fig.  116 


ELECTEICAL  INSTRUMENTS 


157 


in  section  (163),  is  called  an  indicating  wattmeter,  since 
it  gives  the  instantaneous  value  of  the  watts  expended  in  a 
circuit,  just  as  a  voltmeter  and  ammeter  indicate  the  fluctua- 
tion in  voltage  and  current.  The  watt-hour  consumption  in 
any  circuit  could  be  determined  by  means  of  such  a  meter 
by  multiplying  the  average  indication  of  the  meter  for  a 


Fig.  117 


given  time  by  the  time  expressed  in  hours.  An  integrating 
wattmeter  automatically  multiplies  the  average  of  the  in- 
stantaneous readings  by  the  time.  The  Thomson  integrating 
wattmeter,  shown  in  Fig.  117,  is  similar  to  the  dynamometer 
wattmeter,  but  the  movable  coil  rotates.  It  is  really  a  small 
electric  motor  without  any  iron  in  its  working  parts.  The 
revolving  part,  or  armature,  is  the  pressure  coil  and  the 
field  in  which  this  coil  rotates  is  produced  by  the  load  cur- 
rent in  stationary  coils  mounted  outside  of  the  armature. 
The  force  tending  to  produce  rotation  is  proportional  to  the 
product  of  the  two  magnetizing  effects  and  this  is  proper- 


158  PKACTICAL  APPLIED  ELECTRICITY 

tional  to  the  watts  in  the  circuit,  just  as  in  the  case  of 
the  electrodynamometer.  The  magnetizing  effect  of  the  cur- 
rent in  the  armature  is  made  continuous  by  winding  the 
armature  with  a  number  of  coils,  which  are  symmetrically 
placed  on  the  armature  frame  and  connected  to  the  external 
circuit  through  a  small  commutator  and  two  brushes.  The 
current  through  the  armature  coils  is  reversed  at  such  a 
time  that  the  turning  effort  is  always  in  the  same  direction. 

The  speed  of  the  armature  is  made  proportional  to  the 
driving  force  by  mounting,  on  the  same  shaft  that  carries 
the  armature,  a  copper  disk  which  is  arranged  to  revolve  be- 
tween permanent  magnets  and  constitutes  a  small  generator. 
The  torque  required  to  drive  this  disk  is  directly  propor- 
tional to  the  speed,  and  hence,  if  the  torque  produced  by 
the  action  of  the  two  magnetizing  effects  be  doubled,  the 
speed  of  the  meter  will  be  doubled.  The  speed  of  the  meter 
at  any  instant  is  proportional  to  the  product  of  (E)  and  (I), 
or  the  power.  The  average  speed  for  a  unit  of  time,  say  one 
hour,  would  be  proportional  to  the  average  power  times  the 
time  it  acts  (average  E  X  I  X  time  in  hours),  which  gives 
the  value  of  the  energy  in  watt-hours. 

An  indicating  device  is  usually  attached  to  the  meter,  the 
pointers  of  which  are  driven  by  a  worm  that  is  rigidly  fastened 
to  the  shaft  upon  which  the  armature  is  mounted.  The  rela- 
tion between  the  movement  of  the  pointers  on  the  dials  is 
usually  such  that  the  dial  readings  give  the  energy  direct  in 
watt-hours,  or  kilowatt-hours.  In  some  cases,  however,  the 
dial  readings  must  be  multiplied  by  a  constant  in  order  to 
obtain  the  true  watt-hour  or  kilowatt-hour  consumption. 

A  diagram  of  the  connections  of  a  Thomson  watt-hour 
meter  is  shown  in  Fig.  118.  The  coils  (Cj)  and  (C2)  rep- 
resent the  series  coils  connected  in  series  with  the  line  and 
carrying  the  load  current.  The  pressure  circuit,  which  is 
connected  across  the  line,  consists  of  the  resistance  coil 
(S)  and  the  winding  on  the  armature  (A).  The  coil  (S) 
serves  a  double  purpose:  it  prevents  an  excessive  current 
passing  through  the  pressure  circuit  and  it  creates  a  mag- 
netic field  which  is  just  sufficient  to  produce  the  required 
turning  effort  to  overcome  the  static  friction  of  the  meter. 
If  this  magnetic  field  were  not  produced  by  the  coil  (S) 
or  a  similar  coil,  the  armature  of  the  meter  would  not  start 


ELECTEICAL  INSTRUMENTS 


159 


to  rotate  with  a  small  load  current  in  the  coils  (Cj)  and 
(€2),  and  its  indications,  as  a  result,  would  always  be  lower 
than  the  true  value  of  the  energy.  The  magnetic  field  pro- 
duced by  the  coil  (S)  is  in  Lhe  same  direction  as  that  pro- 
duced by  the  current  in  the  coils  (C^)  and  (C2).  The  ef- 
fect of  this  field  on  the  armature  can  be  varied  by  changing 
the  position  of  the  coil  (S)  with  respect  to  the  armature. 
With  this  adjustment,  the  friction  of  the  meter  may  be  prop- 
erly compensated  for  and  it  will  start  to  rotate  with  an 
extremely  small  current  in  the  series  coils.  Meters  of  this 
kind  are  called  integrating  wattmeters,  since  their  dials  in- 
dicate the  average  of  the  product  of  the  instantaneous  power 
times  the  time  that  power 
acts;  or  their  indication  is 
proportional  to  the  energy. 
The  watt-hour  meter  just 
described  will  operate  in 
an  alternating-current  cir- 
cuit, but  not  very  satis- 
factorily on  account  of  the 
inductance  of  the  w  i  n  d- 


Source  of 
Energy 


LoadQ  000 


Fig.  118 


ings. 

167.  Coulomb,  or  Ampere- 
Hour  Meters. — There  are 
several  recording  meters 

on  the  market  whose  indications  are  proportional  to  the  aver- 
age current  through  them  times  the  time  the  current  exists 
in  the  circuit,  and  entirely  independent  of  the  voltage  produc- 
ing the  current.  Such  instruments  are  often  called  coulomb, 
or  ampere-hour  meters.  Meters  of  this  kind  can  be  used  in 
measuring  energy,  when  properly  calibrated,  provided  the 
pressure  producing  the  current  remains  constant.  The  voltage 
of  a  line,  as  a  rule,  is  not  always  the  same,  but  will  fluctuate 
quite  a  number  of  volts  and,  as  a  result,  a  coulomb  meter  will 
not  indicate  the  true  energy. 

The  old  Edison  chemical  meter  was  nothing  more  than  a 
coulomb,  or  ampere-hour  meter.  It  consisted  of  two  zinc 
plates  immersed  in  a  solution  of  zinc  sulphate.  The  quan- 
tity of  electricity  that  had  passed  through  the  meter  was 
determined  by  weighing  the  plates  and,  from  their  change  in 
weight,  the  quantity  was  calculated  by  means  of  the  elec- 


160 


PRACTICAL  APPLIED  ELECTRICITY 


trochemical  equivalent.  Fluctuations  in  line  voltage  pro- 
duced no  effect  upon  the  indications  of  the  meter  directly; 
voltage  changes,  however,  produce  a  change  in  the  value  of 
the  current  and  this  changed  the  meter's  indication.  The 
customer's  bill  was  calculated  on  the  assumption  that  the 
voltage  remained  constant. 

168.  Maximum  Demand  Meters.  —  In  order  to  charge  the 
purchaser  of  electrical  energy  a  fair  amount  for  the  energy 
consumed  in  a  given  time,  it  is  often 
desirable  to  know  the  maximum 
amount  called  for  during  any  time,  in 
order  that  he  may  be  properly  taxed 
or  that  part  of  the  supply  equipment 
that  must  be  held  in  reserve  for  him 
so  that  he  may  take  that  maximum  de- 
mand at  any  time.  An  instrument 
used  in  measuring  the  value  of  this 
maximum  demand  is  called  a  max- 
imum  demand,  or  demand,  rneter. 

The  Wright  demand  meter  is  shown 
in  Fig.  119.  It  consists  of  a  U-shaped 
tube  with  enlarged  ends  and  a  side 
tube  (S)  opening  out  of  one  of  them. 
A  few  turns  of  wire  are  wound  around 
the  enlarged  end  of  the  tube  (A),  that 
has  not  the  side  outlet,  so  that  the  heat 

generated  in  the  wire  due  to  the  passage  of  a  current  through 
it  will  warm  the  air  in  the  chamber.  The  U-shaped  tube  is 
filled  with  liquid  to  about  the  height  shown  in  the  figure.  The 
expansion  of  the  air  in  the  chamber  (A),  due  to  the  heat, 
forces  the  surface  of  the  liquid  in  the  left-hand  leg  of  the  tube 
downward  and  the  surface  of  the  liquid  in  the  right-hand 
one  upward.  If  the  current  strength  is  sufficiently  high  to 
cause  the  liquid  in  the  right-hand  tube  to  rise  to  the  point 
where  the  outlet  tube  is  connected,  the  liquid  will  over- 
flow into  the  tube  (S).  The  greater  the  current  in  the  wind- 
ing about  (A),  the  greater  the  overflow  from  the  tube  (R) 
into  (S),  and  a  scale  properly  graduated  placed  alongside 
the  tube  (S)  will  show  the  maximum  amperage  that  has 
passed  through  the  winding  about  (A).  The  indication  of 
the  instrument  is  rather  slow;  that  is,  it  takes  some  time 


Fig.  119 


ELECTRICAL  INSTRUMENTS 


161 


for  the  liquid  in  (R)  to  rise  to  the  point  where  it  will  over- 
flow into  (S),  even  though  the  proper  current  is  passing 
through  the  winding  about  (A).  This  prevents  the  customer 
being  penalized  due  to  a  momentary  short- 
circuit  on  his  line  or  the  large  current 
taken  for  a  short  time  in  starting  motors. 
The  meter  is  reset,  usually  when  the  con- 
sumer's integrating  meter  is  read,  by  sim- 
ply inverting  the  tube  and  draining  all  of 
the  liquid  out  of  the  tube  (S)  back  into 
the  U-shaped  tube.  Changes  in  the 
temperature  of  the  atmosphere  do  not  in- 
terfere to  any  great  extent  with  the  correct 
registration  of  the  meter,  and  it  will  work 
equally  well  in  either  a  direct-  or  an 
alternating-current  circuit.  The  whole 
instrument  is  placed  in  a  case  that  can 
be  locked  or  sealed,  as  shown  in  Fig.  120, 
so  that  it  cannot  be  reset  by  a  party  not 
authorized  to  do  so. 

CALIBRATION   OF   INSTRUMENTS   . 

169.  Calibration      of     Voltmeters     by 
Means   of   a    Standard    Instrument. — The 
accuracy  of  a  voltmeter's  indications  may 
be  determined  by  connecting  it  in  parallel 
with  another  voltmeter  whose  calibration 
is  known  (called  a  standard),  and  compar- 
ing their  indications  for  various  impressed 
voltages.     The  connections  of  the  instru- 
ments   are    shown    in    Fig.    121,    where    (S)    represents    the 
standard   instrument,    (X)    the   instrument   to   be   calibrated, 
and    (R)    a   suitable  rheostat  for  varying  the   pressure  over 
the  voltmeter  terminals. 

170.  Calibration  of  Voltmeters  by  Means  of  a  Potentiome- 
ter.— The    potentiator    is    a    special    arrangement   for    meas- 
uring   an    electrical    pressure    by    comparison.      It    is    shown 
diagrammatically    in    Fig.    122.      The    pressure    to    be    meas- 
ured is   connected   between  the  terminals    (A — )   and    (A+). 
There    is    a   variable    known    resistance    connected    between 


Fig.  120 


162 


PRACTICAL  APPLIED  ELECTRICITY 


Fig.  121 


these  two  points.  Across  a  portion  of  this  resistance,  such  as 
that  between  the  points  (1)  and  (2),  there  is  connected  a 
shunt  circuit  which  consists  of  a  sensitive  galvanometei 
(G),  a  standard  cell  (SC),  a  contact  key  (K),  and  a  high 
resistance  (H)  that  may  be  easily  cut  in  or  out  of  the  circuit. 

The  operation  of  the  po- 
tentiometer is  as  follows: 

?  L^==a=*%|  First,  assume  it  is  desired 

v55>y  to  know  the  value  of  some 

\  Ck-xO  // 

o 1  ^)  f®  pressure  that  is  connected 

^ • —  to    the    points    (A—)    and 

(A-f).  The  resistance  (R) 
between  the  points  (1)  and 
(2)  should  be  adjusted  to 
1000  (this  need  not  always 
be  1000)  times  the  voltage 
of  the  standard  cell,  which 
is  1.434  for  a  Clark  cell 
at  15°  Centrigrade,  and 
1.018  30  for  a  Weston  nor- 
mal cell.  Assuming  a  Weston  cell  is  used,  then  the  value  of 
the  resistance  in  (R)  will  be  1018.30  ohms.  Now,  there  will  be 
a  difference  in  pressure  between  the  points  (1)  and  (2), 
due  to  the  current  in  the 
resistance  (R)  produced  by 
the  pressure  impressed 
upon  the  terminals  (A — ) 
and  (A+).  The  current 
through  the  resistance  (R) 
is  in  such  a  direction  that 
the  point  (1)  is  at  a  higher 
potential  than  the  point 
(2).  This  difference  in 
pressure  between  the 
points  (1)  and  (2)  would 

tend  to  produce  a  current  in  the  shunt  circuit  when  the  key 
(K)  was  closed.  The  standard  cell,  however,  is  connected  in 
the  circuit  in  such  a  way  that  its  electromotive  force  tends  to 
counteract  the  difference  in  pressure  between  the  points  (1) 
and  (2)  and  there  will  be  no  current  in  the  shunt  circuit  when 
the  drop  in  potential  over  (R)  is  exactly  equal  to  the  e.m.f.  of 


Fig.  122 


ELECTKICAL  INSTRUMENTS 


163 


the  standard  cell.  The  drop  over  the  resistance  (R)  can  be 
varied  by  changing  the  value  of  the  total  resistance  between 
(A—)  and  (A-f).  There  will  be  no  deflection  of  the  galvan- 
ometer when  a  balance  is  obtained.  The  high  resistance  (H) 
should  be  cut  out  of  circuit  for  a  final  adjustment.  The  pur- 
pose of  this  resistance  is  to  protect  the  standard  cell  from 
supplying  too  large  a  current  while  adjusting  the  drop  over 
(R),  which  is  likely  to  change  the  value  of  its  e.m.f.  and  per- 
haps ruin  the  cell.  When  this  balance  is  secured,  there  will  be 
1.018  30  volts  drop  in  pressure  over  1018.30  ohms  in  the  main 
part  of  the  circuit,  or  1  volt  over  every  1000  ohms.  The  total 
difference  in  pressure  between  (A — )  and  (A+)  will  then 
be  equal  to  the  resistance  between  (A — )  and  (A+)  divided 
by  1000. 

Ordinary  resistance  boxes  may  be  used  for  the  resistances 
shown  in  the  scheme,  but  commercial  forms  of  the  poten- 
tiometer are  constructed  with  all  the  keys,  resistances,  etc., 
contained  in  a  single  case. 

171.  Calibration  of  Ammeters  by  Means  of  a  Standard  In- 
strument.— An  ammeter  may  be  calibrated  by  connecting  it 
in  series  with  a  standard 

instrument  and  comparing 
their  indications  for  differ- 
ent values  of  current.  The 
scheme  of  connections  is 
shown  in  Pig.  123,  in  which 
(S)  represents  the  stand- 
ard instrument,  (X)  the  in- 
strument to  be  calibrated, 
(B)  a  storage  battery  or 
some  source  of  electrical 
energy,  and  (R)  a  rheostat 

suitable  for  changing  the  value  of  the  current  in  the  circuit  by 
a  change  in  its  resistance. 

A  standard  resistance  may  be  connected  in  series  with  an 
ammeter  and  the  current  in  the  circuit  determined  by  divid- 
ing the  drop  over  the  resistance — which  may  be  determined 
by  means  of  a  voltmeter  or  a  potentiometer — by  the  resist- 
ance of  the  standard  resistance. 

172.  Calibration  of  a  Wattmeter  by  Means  of  a  Voltmeter 
and    an    Ammeter. — The   connections   for   calibrating   a   watt- 


r— |  h|  \]  K^WVWVWW 


Fig.   123 


164 


PRACTICAL  APPLIED  ELECTRICITY 


meter  or  a  watt-hour  meter  by  means  of  a  voltmeter  and 
an  ammeter  are  shown  in  Fig.  124.  The  current  in  the 
series  coil  of  the  wattmeter  exceeds  that  in  the  ammeter  by 
an  amount  equal  to  the  current  in  the  voltmeter.  The  true 
power,  then,  should  be  calculated  by  adding  to  the  ammeter 
reading  (Ia)  the  voltmeter  current  (Iv)  and  multiplying  the 
sum  by  the  voltmeter  reading  (E),  or 


W  =  (la  + 


E 


(97) 


The  per  cent  error  introduced  by  not  taking  the  voltmeter 


Pressure  Coil 
Series  Coils 


Load 


£66000 


Fig.  124 

current  into  account  is  very  small,  except  in  the  calibra- 
tion of  low  reading  wattmeters. 

When  a  separate  source  of  current  and  pressure  are  used, 
the  current  taken  by  the  voltmeter  produces  no  error  and 
the  true  power  is  given  by  the  equation 

W  =  EXI  (98) 

The  indication  of  the  dial  on  a  watt-hour  meter  can  be 
checked  by  maintaining  the  e.m.f.  and  current  constant  for 
a  given  time  and  noting  the  difference  in  the  dial  read- 
ings before  and  after  the  test.  The  energy  indicated  on 
the  dial  should  equal  the  product  of  (E),  (I),  and  (t),  or 

k.w.  hours  =  E  X  I  X  t  (99) 

The  time  (t)  in  the  above  equation  should  be  in  hours.  The 
dial  indication  can  be  accurately  determined  from  the  num- 


ELECTKICAL  INSTEUMENTS 


165 


ber  of  revolutions  of  the  armature,  if  the  number  of  revolu- 
tions of  the  armature  per  unit  indication  on  the  dial  is  known. 
This  relation  is  called  the  gear  ratio,  and  once  determined 
it  can  be  used  in  succeeding  tests. 

173.  Calibration  of  Wattmeters  by  Means  of  Standard 
Wattmeter. — Two  wattmeters  are  shown  connected  in  the 
same  circuit  in  Fig.  125.  The  instrument  (S)  is  a  standard, 


JLL 

X 

j 

5 

I 

Load 

00 

<y 

00 

PV 

00      00 

rt 

I 

L  k  k 

I 

f  (  (   000 

Fig.   125 

or  one  whose  calibration  is  known,  while  (X)  is  an  instru- 
ment to  be  calibrated.  If  the  series  coils  of  the  two  instru- 
ments have  the  same  resistance,  the  pressure  impressed  upon 
the  pressure  circuits  of  the  two  meters  is  the  same,  when  the 
connections  are  made,  as  shown  in  the  figure.  The  same  load 
current  exists  in  the  series  coils  of  both  instruments  and  the 
indication  of  (X)  can,  therefore,  be  determined  in  terms  of 
the  indication  of  (S). 


CHAPTEE  IX 

THE  DIRECT-CURRENT  GENERATOR 

174.  The  Dynamo. — The  dynamo  is  a  machine  for  convert- 
ing mechanical  energy  into  electrical  energy,  or  electrical  en- 
ergy into  mechanical  energy  by  means  of  electromagnetic  in- 
duction, the  principles  of  which  were  discovered  by  Faraday 
about  1831.     The  dynamo,  when  used  to  transform  mechan- 
ical energy  into  electrical  energy,  is  called  a  generator,  and 
when  used  to  transform  electrical  energy  into  mechanical,  it 
is  called  a  motor.    The  generator  does  not  create  electricity, 
but  simply  imparts  energy  to  it,  just  as  energy  is  imparted 
to  the  electricity  as  it  passes  through  the  primary  cell.     The 
e.m.f.  which  is  generated  in  the  dynamo  produces  a  current 
in  a  closed   circuit  connected  to  the  machine  and  this  cur- 
rent will  pass  from  a  higher  to  a  lower  potential  in  the  ex- 
ternal circuit  and  from  a  lower  to  a  higher  potential  in  the 
internal    circuit    of    the    machine    itself.      This    corresponds 
to  the  flow  of  water  through  a  pipe  connected  to  a  pump. 
In  the  external  circuit,  the  water  flows  from  a  higher  to  a 
lower  pressure,  while  the  action  of  the  pump  causes   it  to 
flow  from  a  lower  to  a  higher  pressure  through  the  pump 
itself. 

The  dynamo  consists  fundamentally  of  two  parts — a  mag- 
netic field,  which  may  be  produced  by  permanent  magnets  or 
electromagnets,  and  an  armature,  which  consists  of  a  coil  or 
number  of  coils  usually  wound  or  mounted  on  an  iron  core 
and  so  arranged  that  they  may  be  revolved  or  moved  in  the 
magnetic  field  of  the  machine.  The  movement  of  the  coils 
in  the  magnetic  field  results  in  the  conductor  forming  the 
ceils  cutting  the  magnetic  lines  of  the  field  and  an  e.m.f.  is 
induced  in  the  winding. 

175.  Kinds  of  Generators. — Generators  may  be  grouped  into 
two  main  classes,  depending  upon  the  nature  of  their  output; 
viz.,  direct-current  and  alternating-current. 

166 


THE  DIRECT-CURRENT  GENERATOR  167 

The  current  in  a  circuit  connected  to  a  direct-current  gen- 
erator is  in  the  same  direction  all  the  time,  while  in  the  case 
of  the  alternating-current  generator  it  is  continuously  revers- 
ing in  direction.  This  chapter  will  deal  with  the  direct- 
current  machine,,  the  discussion  of  the  alternator  being  de- 
ferred to  a  later  chapter. 

The  mechanical  construction  of  dynamos  permits  their  be- 
ing divided  into  three  classes,  the  fundamental  electrical  prin- 
ciple being  the  same  in. each  case. 

(a)  Revolving  armature  and  stationary  field  magnet. 

(b)  Revolving  field  and  stationary  armature. 

(c)  Armature  and  field  winding  both  stationary,  but  con- 
structed so  that  an  iron  core  may  be  revolved  near  them. 

The  external  circuit  is  connected  to  the  armature  winding 
in  the  first  class  by  means  of  collector  rings,  see  section  (177), 
or  by  means  of  a  commutator,  see  section  (178),  while  the  con- 
nection to  the  field  winding  is  permanent  since  it  is  stationary. 
In  the  second  class  the  armature  is  permanently  connected 
to  the  external  circuit,  and  the  connection  is  made  to  the 
field  winding  by  means  of  slip  rings.  There  are  no  moving 
conductors  in  the  third  class,  but  the  magnetic  flux  through 
the  armature  winding  that  is  produced  by  the  current  in  the 
field  winding  is  caused  to  change  in  value  by  changing  the 
position  of  a  part  of  the  magnetic  circuit.  This  part  of  the 
magnetic  circuit  is  called  the  inductor  and  it  is  arranged  so 
that  it  may  be  rotated  near  the  armature  and  field  windings. 

Direct-current  generators  may  also  be  divided  according  to 
their  output,  viz., 

(a)  Constant-Current   Generators. 

(b)  Constant-Potential  Generators. 

The  output  of  the  constant-current  generator  is  at  a  con- 
stant current  and  variable  pressure,  while  the  output  of  the 
constant-potential  generator  is  at  a  constant  potential  and 
•variable  current. 

176.  Simple  Dynamo. — If  a  single  loop  of  wire,  such  as 
(ABCD),  Fig.  126,  be  revolved  about  an  axis,  such  as  (EF), 
in  the  magnetic  field  of  a  permanent  magnet,  or  an  electro- 
magnet, as  shown  in  the  figure,  there  will  be  an  electromotive 
force  induced  in  the  two  sides  of  the  loop  (AB)  and  (CD). 
This  induced  electromotive  force  will  produce  a  current  in 
the  loop  if  the  conductor  forming  the  loop  be  closed.  The 


168 


PRACTICAL  APPLIED  ELECTRICITY 


direction  of  the  induced  e.m.f.  in  the  two  sides  of  the  loop 
may  be  determined  by  a  simple  application  of  Fleming's  dy- 
namo rule,  as  given  in  section  (118).  The  motion  of  one  side 
of  the  loop,  such  as  (AB),  with  respect  to  the  field  is  just  the 
reverse  of  the  motion  of  the  other  side  (CD).  As  a  result 
of  this  difference  in  motion  of  the  two  sides  of  the  loop  with 
respect  to  the  magnetic  field,  the  e.m.f.  induced  in  one  side 
of  the  loop  will  be  from  the  observer,  while  that  induced  in 


Fig.  126 


the  other  side  will  be  toward  the  observer.  These  two  e.m.f.'s 
are  acting  in  series  and,  since  their  directions  are  opposite 
with  respect  to  the  position  of  the  observer,  they  both  tend  to 
produce  a  current  in  the  same  direction  around  the  loop.  The 
value  of  the  current  in  the  loop  will  depend  upon  the  induced 
e.m.f.  and  the  ohmic  resistance  of  the  loop.  There  will  be 
no  induced  e.m.f.  in  the  ends  of  the  loop  since  they  do  not 
cut  any  of  the  magnetic  lines. 

177.  Simple  Alternator. — If  the  loop,  shown  in  Fig.  126,  be 
cut  at  one  end  and  the  two  ends  thus  formed  be  connected 
to  two  metallic  rings  (Rj)  and  (R2)  mounted  on  the  shaft 
and  insulated  from  each  other,  as  shown  in  Fig.  127,  the  com- 
bination will  constitute  what  is  called  a  simple  alternator- 
An  external  circuit  can  be  connected  to  the  coil  or  armature 
by  means  of  two  brushes  (B^  and  (B2)  that  rub  on  the  two 
metallic  rings.  The  e.m.f.  induced  in  the  armature  will  now 
produce  a  current  through  the  external  circuit  and  the  armature 
in  series.  The  value  of  this  current  will,  as  in  the  previous 
case,  depend  upon  the  value  of  the  induced  e.m.f.  and  the 
ohmic  resistance  of  the  entire  circuit. 

The  e.m.f.  induced  in  the  two  sides  of  the  loop  at  any  time 


THE  DIEECT-CUBEENT  GENEEATOE 


169 


will  depend  upon  the  number  of  magnetic  lines  cut  in  one 
second,  or  the  rate  at  which  the  lines  are  being  cut.  This 
rate  of  cutting  of  magnetic  lines  will  depend  upon  the  length 
of  the  two  sides  of  the  loop,  the  strength  of  the  magnetic 
field,  and  the  direction  in  which  the  conductor  is  moving  with 
respect  to  the  magnetic  field.  Assuming  the  strength  of  the 
magnetic  field  is  uniform  and  it  remains  constant,  and  the 
loop  revolves  about  its  axis  at  a  constant  rate,  then  the  e.m.f. 
induced  in  the  loop  will  change  in  value,  due  only  to  a  change 
in  the  direction  of  motion  of  the  two  sides  of  the  loop  with 
respect  to  the  magnetic  field.  Thus,  when  the  loop  is  in  the 


0 


90 


Fig.   128 


Fig.   129 


horizontal  position,  the  direction  of  the  field  also  being 
horizontal,  the  two  sides  of  the  loop  will  be  moving  in  a 
path,  just  for  an  instant,  perpendicular  to  the  direction  of 
the  field,  and  the  number  of  lines  of  force  that  the  two  sides 
of  the  loop  will  cut,  due  to  a  given  motion  of  the  coil,  will 
be  a  maximum.  When  the  loop  is  in  a  vertical  position,  or 
perpendicular  to  the  direction  of  the  magnetic  field,  any  small 
movement  of  the  loop  will  result  in  no  lines  of  force  being 
cut  by  the  two  sides  and,  hence,  no  e.m.f.  will  be  induced.  The 
value  of  the  e.m.f.  induced  in  the  two  sides  of  the  loop  for 
positions  between  those  just  given,  will  depend  upon  the  part, 
or  component,  of  the  motion  that  is  perpendicular  to  the 
direction  of  the  magnetic  field.  This  component  is  propor- 
tional to  the  sine  of  the  angle  between  the  position  of  the 
coil  and  the  plane  perpendicular  to  the  magnetic  field.  The 
sine  of  an  angle  (9),  see  Fig.  128,  is  equal  to  the  length  of  the 


170  PRACTICAL  APPLIED  ELECTEICITY 

line  (a)  divided  by  the  length  of  the  line  (b).  This  relation 
remains  the  same  regardless  of  the  size  of  the  triangle  so 
long  as  the  angle  (0)  does  not  change  in  value.  From  the 
table  of  "Trigonometrical  Functions"  in  Chapter  20,  may  be 
found  the  values  of  the  sines  of  different  angles  from  0° 
to  90°. 

A  curve  can  be  drawn  which  will  show  graphically  the  rela- 
tion between  the  induced  e.m.f.  in  the  coil  and  its  angular 
position  with  respect  to  some  reference  plane,  say  the 
plane  parallel  to  the  magnetic  field.  Draw  a  line  (AB), 
Fig.  129,  and  divide  this  line  into,  say,  90  equal  parts,  each 
part  will  then  correspond  to  four-degrees  movement  of  the 
coil  about  its  axis.  Starting  with  the  coil  in  a  plane  per- 
pendicular to  the  magnetic  field,  and  let  this  correspond  to  the 
point  (A)  in  the  figure,  the  e.m.f.  induced  in  the  coil  for  any 
angular  displacement  from  this  position  should  be  measured 
off  to  a  convenient  scale  on  a  line  drawn  through  the  point 
on  (AB),  corresponding  to  the  displacement  of  the  coil.  Thus, 
the  e.m.f.  will  be  a  maximum  when  the  coil  has  rotated 
through  an  angle  of  90°,  since  the  value  of  the  sine  of  the 
angular  displacement  is  increasing  up  to  this  point.  It  then 
decreases  as  the  angle  increases  from  90°  to  180°  and  becomes 
equal  to  zero  when  the  coil  has  rotated  through  180°.  The 
direction  of  the  movement  of  the  two  sides  of  the  loop  with 
respect  to  the  magnetic  field  changes  just  as  the  coil  passes 
through  its  180°  position  and,  as  a  result,  the  direction  of  the 
induced  e.m.f.  changes.  The  numerical  values  of  the  e.m.f. 
for  the  second  180°  are  identical  to  those  for  the  first  180°, 
but  they  are  opposite  in  sign.  The  difference  in  sign  is 
represented  in  the  curve  by  drawing  the  second  part  of  the 
curve  below  the  horizontal  line. 

178.  Simple  Direct-Current  Dynamo. — Purpose  of  the  Com- 
mutator.— The  e.m.f.  induced  in  the  loop  of  wire  described 
in  the  previous  section  can  be  made  to  produce  a  direct  cur- 
rent— one  that  is  constant  in  direction  in  the  external  circuit — 
in  the  following  way:  Suppose  the  two  continuous  metallic 
rings  be  replaced  by  a  single  ring  composed  of  two  parts  that 
are  insulated  from  each  other,  the  distance  between  the  ends 
of  the  two  parts  composing  the  rings  being  small  in  compari- 
son to  the  total  circumference  of  the  combined  ring.  If  the 
two  ends  of  the  loop  be  connected  to  these  two  parts  of  the 


THE  DIEEOT-CUEEENT  GENEEATOE 


171 


ring,  which  we  shall  call  segments,  and  two  brushes  that 
are  insulated  from  each  other  be  so  mounted  with  respect  to 
each  other  and  the  ring  that  they  rest  upon  the  insulation 
between  the  segments  when  the  e.  m.  f.  induced  in  the  coil  is 
zero,  the  connection  of  the  external  circuit  with  respect  to 
the  loop  will  be  reversed  at  the  same  instant  the  direction  of 
the  induced  e.m.f.  in  the  loop  changes.  This  results  in  the 
induced  e.m.f.  in  the  coil  always  tending  to  send  a  current 
through  the  external  circuit  in  the  same  direction.  The  proper 
arrangement  of  the  loop,  segments,  and  the  brushes  is  shown 
in  Fig.  130.  Such  a  machine  is  called  a  simple  direct-current 
dynamo,  because  it  delivers  a  direct  current  to  the  external 
circuit.  The  two-part  ring  constitutes  a  simple  commutator 
of  two  segments,  and  its  purpose,  as  pointed  out,  is  to  reverse 
the  connection  of  the  external  circuit  with  respect  to  the 


90°  180°  270°          360" 


Fig.    131 


armature  winding,  or  vice  versa,  so  that  the  induced  e.m.f.' 
in  the  winding  will  send  a  direct  current  through  the  external 
circuit.  A  curve  representing  the  value  of  the  e.m.f.  impressed 
upon  the  external  circuit  when  the  two-part  commutator  is 
used  is  shown  in  Fig.  131.  An  e.m.f.  such  as  that  represented 
in  Fig.  131  is  called  a  pulsating  e.m.f.,  because  it  pulsates  or 
changes  from  zero  to  a  maximum  and  back  to  zero  at  regular 
intervals. 

179.  Multiple-Coil  Armatures. — If  the  armature  of  a  direct- 
current  generator  were  constructed  with  a  single  coil  com- 
posed of  one  or  more  turns,  the  current  delivered  by  such  a 
machine  would  pulsate  in  value  the  same  as  the  e.m.f.,  as 


172 


PRACTICAL  APPLIED  ELECTRICITY 


18 


Fig.   132 


shown  in  Fig.  131.  The  operation  of  such  a  machine  would 
be  very  unsatisfactory  in  a  great  many  cases.  Fortunately  the 
e.m.f.  between  the  brushes  of  the  machine  can  be  made  more 
nearly  constant  in  value  in  the  following  way: 

Suppose  two  closed  coils 

A  D  (A)  and  (B)  be  placed  on 

the  armature  at  right  an- 
gles to  each  other,  then 
the  induced  e.m.f.  in  one 
of  them  will  be  a  maxi- 
mum when  the  induced 
e.m.f.  in  the  other  one  is 
zero.  Now  as  the  arma- 
ture rotates  from  such  a 
position  that  the  plane  of 
coil  (A)  is  perpendicular 
to  the  magnetic  field — zero 
e.m.f.  induced  in  it — and 
the  plane  of  coil  (B)  is 

parallel  to  the  magnetic  field — maximum  induced  e.m.f.  in 
it — the  induced  e.m.f.  in  coil  (A)  will  increase  and  the 
induced  e.m.f.  in  coil  (B)  will  decrease,  and  this  action  will 
continue  until  the  armature  has  turned  through  an  angle 
of  90°.  After  the  armature  has  turned  through  an  angle  of 
90°,  the  e.m.f.  in  coil  (A)  is  a  maximum  and  that  in  coil  (B) 
is  zero.  For  the  next  90°,  the  e.m.f.  in  coil  (A)  is  decreasing 
and  the  e.m.f.  in  coil  (B)  is  increasing,  but  in  the  opposite  di- 
rection. The  corresponding  values  of  induced  e.m.f.  will  occur 
in  the  two  coils  at  inter- 
vals which  differ  in  value 
by  one-fourth  revolution, 
or  90°.  The  two  curves  (A) 
and  (B)  in  Fig.  132  show 
the  relation  of  the  e.m.f.'s 
in  the  two  coils. 
If  now  a  four-segment 


180° 
Fig.  133 


no" 


360 


o          9(r 

commutator   be   used    and 
two  coils  be  symmetrically 

placed  on  the  armature,  the  terminals  of  each  coil  being  con- 
nected to  opposite  commutator  segments,  the  e.m.f.  between 
the  brushes  of  the  machine  will  never  fall  to  zero  value  but 


THE  DIRECT-CURRENT  GENERATOR  173 

will  be  of  the  form  shown  by  the  full  line  in  Fig.  133,  when 
the  brushes  are  properly  placed  with  respect  to  the  commu- 
tator. The  e.m.f.  can  be  made  more  nearly  constant  by 
placing  more  coils  on  the  armature  in  such  a  position  with 
respect  to  the  first  ones  that  the  induced  e.m.f.  in  them  does 
not  reach  a  maximum  or  zero  value  at  the  same  time  it  does 
in  the  others,  and  connecting  them  in  such  a  way  that  the 
induced  e.m.f.  in  all  of  the  coils  acts  in  series  and  in  the 
same  direction  as  far  as  the  external-  circuit  is  concerned. 

180.  The  Armature  of  a  Dynamo. — The  loops  of  wire,  or 
coils,  in  which  the  e.m.f.  is  induced  by  a  movement  of  them 
with  respect  to  the  magnetic  field,  together  with  the  iron  parts 
upon  which  they  are  mounted,  insulating  material,  and  slip 
rings  or  commutator — in  the   cases  where  the  coils  move — 
constitute  what  is  called  the  armature  of  a  dynamo.  The  classi- 
fication of  armatures,  their  construction,  and  methods  of  wind- 
ing will  be  taken  up  in  detail  in  the  chapter  on  "Armatures 
for  Direct-Current  Dynamos." 

181.  Magnetic    Field    of    a 
Dynamo. — In  the   majority  of 
cases    the    magnetic    field    of 
a    dynamo    is    produced    by 
electromagnets.     In  the  case 
of    magnetos,     however,    the 
magnetic   field  is   created  by 
several    powerful    permanent 
horseshoe   magnets.     Such   a 
machine     is     shown    in    Fig. 
134.       Small     machines     are 

usually  bipolar,  that  is,  they  Fig.  134 

have     one     N-pole     and     one 

S-pole  which  create  the  magnetic  field  in  which  the  armature 

rotates.     These  magnetic  fields  assume  a  number  of  different 

forms,  a  few  of  which  are  shown  in  Fig.  135. 

In  large  machines  it  is  customary  to  use  multipolar  field 
magnets  in  which  any  even  number  of  poles  are  arranged 
alternately  around  the  armature.  The  magnetic  circuit  of  a 
machine  whose  field  is  created  by  an  electromagnet  usually 
consists  of. five  parts,  as  shown  in  Fig.  136.  (1)  The  field 
cores  (C)  are  the  centers  of  the  coils  carrying  the  magnetiz- 
ing current.  (2)  The  yoke  (Y)  connects  the  field  cores 


174 


PKACT1CAL  APPLIED  ELECTKICITY 


together  at  one  end,  as  shown  in  the  figure.  (In  some 
machines  there  is  no  yoke  in  the  magnetic  circuit,  see  Fig. 
135  A.)  (3)  The  pole  pieces  (P)  are  the  metallic  parts  of  the 
magnetic  circuit  next  to  the  armature.  They  are  usually  cut 
to  conform  to  the  curvature  of  the  armature  and  in  some 
cases  are  an  entirely  different  piece  of  metal  than  the  field 
cores,  being  fastened  to  the  end  of  the  field  cores  by  means 
of  bolts.  The  surface  of  the  pole  pieces  next  to  the  armature 


D 


Fig.  135 


Is  called  the  pole  face;  and  the  projecting  edges,  when  so 
constructed,  are  called  the  horns.  (4)  The  air  gap  (G)  is  the 
space  between  the  pole  face  and  the  armature  core.  (5)  The 
armature  core  conducts  the  magnetic  lines  from  one  air  gap 
to  another. 

The  coils  carrying  the  magnetizing  current  may  be  placed 
on  the  magnetic  circuit  as  shown  in  Fig.  135  D  or  they  may 
be  placed  on  the  magnetic  circuit  as  shown  in  Fig.  135  C. 
When  the  field  windings  are  placed,  as  shown  in  Fig.  135  D, 
the  magnetomotive  force  created  by  the  current  in  one  wind- 


THE  DIRECT-CURRENT  GENERATOR 


175 


ing  is  in  series  with  that  created  in  the  other  winding,  or  the 
magnetomotive  force  on  any  magnetic  circuit  is  that  produced 
by  two  windings  in  series.  If  the  windings  be  placed  upon 
the  magnetic  circuit,  as  shown  in  Fig.  135  C,  the  magneto- 
i  motive  force  acting  on  each  magnetic  circuit  would  be  that 
of  a  single  coil.  This  results  in  only  half  the  ampere-turns 
per  coil  being  required  when  they  are  placed  as  shown  in 
Fig.  135  D,  as  would  be  required  if  the  coils  were  placed  as 
shown  in  Fig.  135  C. 

182.     Materials   Used    in  the   Construction   of  the    Magnetic 
Circuit.— There  are  three  materials  that  are  commonly  used 

in  the  construction  of  the 
magnetic  circuit  of  a  dyna- 
mo—  cast  iron,  wrought 
iron,  and  cast  steel.  There 
are  a  number  of  factors 
which  govern  the  selection 
of  the  materials  to  be  used 
in  a  particular  machine, 
such  as  initial  cost,  weight, 
efficiency  demanded  b  y 
purchaser,  regulation,  etc. 
The  cheapest  of  the 
above  materials  is  cast 
iron  and  it  is  the  poorest 
of  them  all  magnetically. 

So  the  saving  in  the  initial  cost  of  the  iron  per  pound  would 
more  than  likely  be  offset  by  the  fact  that  a  larger  bulk  of  cast 
iron  would  be  required  to  form  a  certain  magnetic  circuit  than 
would  be  required  if  wrought  iron,  for  example,  were  used. 
There  would  also  be  an  increase  in  the  cost  of  copper  required 
to  magnetize  the  large  cast-iron  core,  since  the  length  of  each 
turn  would  be  more  than  when  some  better  magnetic  material 
was  used. 

Wrought  iron,  on  the  other  hand,  is  the  best  magnetic 
material  and  at  the  same  time  the  most  expensive.  It  is  used 
where  economy  in  weight  and  reduction  of  cross-section  are 
desired.  Machines  used  aboard  ships  or  electric  automobiles, 
etc.,  are  usually  made  of  wrought  iron  on  account  of  the  large 
reduction  in  weight,  which  is  a  more  important  factor  than 
the  initial  cost. 


Fig.   136 


176  PBACT1CAL  APPLIED  ELECTEICITY 

Cast  steel  occupies  a  place  intermediate  between  cast  iron 
and  wrought  iron  both  in  cost  and  magnetic  properties. 
Machines  are,  as  a  rule,  constructed  of  more  than  one  mate- 
rial. Thus  the  field  cores  will  be  of  wrought  iron,  as  that 
would  mean  a  saving  in  copper  since  the  length  of  wire  per 
turn  would  be  less  than  if  cast  iron  were  used;  the  yoke  may 
be  of  cast  iron  as  its  area  can  be  made  much  larger  than  that 
of  the  field  cores  and  this  increase  in  area  will  add  strength 
to  the  machine.  The  armature  core  is  usually  constructed  of 
wrought-iron  sheets,  so  as  to  reduce  the  eddy-current  loss  to 
a  minimum;  the  pole  shoes  may  be  cast  or  they  are  sometimes 
laminated  in  order  to  reduce  the  eddy-current  loss  in  them. 

183.  Magnetic   Leakage,   Shape  of    Magnetic   Circuit. — The 
total  number  of  magnetic  lines  created  by  the  current  in  the 
field  winding  do  not  pass   through  the  armature   core,   and 
therefore,  they  are  not  all  useful  in  inducing  an  e.m.f.  in  the 
armature  winding.    The  ratio  of  the  total  number  of  magnetic 
lines  created  to  the  number  that  are  actually  useful  in  gen- 
erating an  e.m.f.  is  called  the  leakage  coefficient.     The  value 
of  this  coefficient  can  never  be  less  than  unity  and  in  the 
case  of  poorly  designed  machines,  it  will  reach  a  value  as 
high  as  1.4. 

The  value  of  this  coefficient  can  be  reduced  by  constructing 
the  magnetic  circuit  so  it  will  be  as  short  as  possible,  or  of 
low  reluctance,  and  without  abrupt  turns.  Placing  the  field 
winding  upon  or  near  that  part  of  the  magnetic  circuit  offer- 
ing the  greatest  reluctance  will  also  reduce  the  value  of  the 
leakage  coefficient. 

184.  Value  of  Induced   E.M.F.  in  Armature  Winding.— The 
induced   e.m.f.    in   an   armature   winding    depends   upon   the 
following  factors: 

(a)  The  useful  flux  (<i>)  per  pole  of  the  machine. 

(b)  The  number    of    poles    (p)    composing    the    magnetic 

circuit. 

(c)  The  total  number  of  inductors    (Z)    on   the  armature. 

(d)  The  number  of  paths  (b)  in  parallel  through  the  arma- 

ture. 

(e)  The  speed  (s)  in  revolutions  per  second. 

(f)  The  number  of  magnetic  lines   (108)  that  must  be  cut 

per  second  in  order  that  there  be  an  e.m.f.  of  one 
volt  induced. 


THE  DIEECT-CUBEENT  GENEEATOE  177 

These  factors  can  all  be  combined  in  a  simple  equation  which 
will  give  the  value  of  (E)  in  volts  between  the  brushes  of 
the  machine  when  it  is  operating  without  load,  or  when  it  is 
delivering  no  current. 

$  X  P  X  Z  X  s 
E  =  -  (100) 

108  x  b 

The  value  of  (b)  in  the  above  equation  will  depend  upon  the 
type  of  winding  on  the  armature.  For  a  simple  lap  winding 
(singly  re-entrant)  it  is  equal  to  the  number  of  poles  and  for 
a  simple  wave  winding  (singly  re-entrant)  it  is  always  two 
regardless  of  the  number  of  poles.  This  will  be  taken  up 
again  in  the  chapter  on  "Armature  Winding." 

Example. — A  six-pole  generator  is  operating  at  900  revolu- 
tions per  minute.  The  useful  flux  per  pole  is  4  000  000  lines. 
The  armature  has  a  simple  lap  winding  (singly  re-entrant) 
of  198  inductors.  What  e.m.f.  will  be  generated? 

Solution. — First  obtain  the  value  of  the  speed  in  revolutions 
per  second  by  dividing  900  by  60,  or 

900  -f-  60  =  15 

The  machine  is  then  running  at  15  revolutions  per  second. 
Since  the  winding  on  the  armature  is  a  simple  lap  winding, 
the  value  to  substitute  for  (b)  in  equation  (100)  is  equal  to 
the  number  of  poles,  or  6.  Substituting  the  values  of  the 
various  quantities  in  equation  (100)  gives 

4  000  000  X  6  X  198  X  15 
E=  -  =  118.8 

100  000  000  X  6 

Ans.     118.8  volts. 

185.  Separate  Excitation  and  Self-Excitation  of  a  Genera- 
tor.— There  are  two  methods  by  which  the  electromagnets  of 
the  generator  may  be  energized,  and  they  are 

(a)  Separate  excitation. 

(b)  Self-excitation. 

In  the  case  of  separate  excitation,  the  field  windings  of  the 
machine  are  connected  to  some  source  of  energy,  other  than 
the  dynamo  under  consideration,  such  as  a  storage  battery 
or  another  dynamo,  and  the  current  in  the  field  winding  is 
independent  of  the  e.m.f.  generated  by  the  machine  that  is 


178 


PEACTICAL  APPLIED  ELECTK1CITY 


being  excited.  The  field  current  is  adjusted  in  value  by 
changing  the  value  of  the  resistance  in  the  field  circuit,  which 
is  accomplished  by  what  is  known  as  a  field  rheostat,  or  by 
changing  the  e.m.f.  of  the  generator  that  is  supplying  the 
current  to  the  field.  The  connections  for  separate  excitation 
are  shown  diagrammatically  in  Fig.  137.  The  rheostat  (Rj) 
is  connected  in  series  with  the  field  of  the  main  generator 


(G).  The  field  of  the  main  generator  may  be  connected  to 
either  the  storage  battery  (B)  or  the  small  generator  (E), 
which  is  called  the  exciter.  A  rheostat  (R2)  is  connected  in 
series  with  the  field  of  the  generator  (E)  and  by  means  of  this 
rheostat  the  voltage  generated  in  the  armature  of  the  exciter 
can  be  changed,  and  hence  the  current  in  the  field  of  the 
generator  (G),  if  (E)  is  supplying  current  to  the  field. 

There  are  three  different  methods  of  self-excitation  and 
they  will  each  be  taken  up  in  turn  in  the  following  three 
sections. 

186.     Shunt -Wound     Generator. — 

A/WWW        ^e  field  winding  in  the  case  of  a 

~T  \  p         shunt-wound  generator  consists  of  a 

(G)    jo   Shunt          large  number  of  turns  of  relatively 

]     Sr      1    field  small   wire   that   may   be   connected 

l__/ JWinding        directly  across  the  terminals  of  the 

Fig.  138  machine.     The    potential    difference 

between   the   two   terminals    of    the 

machines  produces  a  current  in  the  field  windings,  which  is 
regulated  in  value  by  a  resistance  or  rheostat.  A  diagram  of 
the  connections  of  a  self-excited  shunt  machine  is  given  in 
Fig.  138. 

187.  Series-Wound  Generator. — The  field  winding  in  the 
case  of  a  series-wound  generator  consists  of  a  few  turns  of 
large  wire  connected  directly  in  series  with  the  armature  and 


THE  DIRECT-CURRENT  GENERATOR 


179 


load.  The  current  in  the  field  windings  of  a  machine  of  this 
kind  is  of  the  same  value  as  the  current  through  the  load.  A 
diagram  of  the  connections  of  a  series-wound  machine  is 
given  in  Fig.  139. 


~\ 


Fig.  139 


Fig.  140 


188.  Compound-Wound  Generator.— In  the  case  of  a  com- 
pound-wound generator,  the  field  windings  consist  of  two  sets 
of  coils.  The  coils  of  one  set  consist  of  a  few  turns  of  large 
wire  connected  in  series  with  the  armature  and  the  load;  the 
coils  of  the  other  set  consist  of  a  large  number  of  turns  of 


j 


Fig.   141 


small  wire,  all  connected  in  series  across  the  terminals  of  (he 
machine.  The  compound  generator  is  nothing  more  than  a 
combination  of  a  shunt  and  series  generator. 

When  the  shunt  winding  is  connected  directly  across  the 
armature,  as  shown  in  Fig.  140,  the  machine  is  called  a  short 
shunt;  when  it  is  connected  across  the  armature  and  the 
series  field,  as  shown  in  Fig.  141,  the  machine  is  called  a  long 


PRACTICAL  APPLIED  ELECTEICITY 

shunt.  In  the  case  of  a  long  shunt  the  current  in  the  shunt 
field  passes  through  the  series  field  in  completing  its  circuit 
through  the  armature;  while  in  the  case  of  a  short  shunt,  the 
current  in  the  shunt  field  passes  directly  through  the  arma- 
ture without  passing  through  the  series  field.  The  current  in 
the  shunt  field  can  be  regulated  by  a  rheostat  (R),  while  the 
current  in  the  series  field  depends  upon  the  current  in  the 
load  to  which  the  machine  is  connected. 

189.  Armature  Reaction. — When  a  dynamo  is  operating 
under  a  load,  the  current  in  the  armature  will  produce  a 
magnetizing  effect  upon  the  field  of  the  machine  and  this 
effect  is  called  armature  reaction.  The  direction  of  this  mag- 
netizing effect  due  to  the  armature  current  can  be  determined 
as  follows:  Take  a  simple  drum  armature  with  twelve  coils 
equally  spaced  around  the  core  and  revolving  in  a  bipolar 
magnetic  field.  (A  cross-section  through  such  an  armature 
and  field  is  given  in  Fig.  142.)  The  induced  e.m.f.  in  the 
armature  inductors  on  the  right  of  a  plane  (AC),  drawn 
perpendicular  to  the  direction  of  the  magnetic  field,  will  be 
just  the  reverse  of  the  direction  of  the  induced  e.m.f.  in  the 
conductors  to  the  left  of  the  plane  (AC).  The  induced  e.m.f. 
in  the  conductors  is  zero  when  they  are  in  the  plane  (AC),  and 
it  changes  in  direction  as  the  conductors  pass  from  one  side 
of  the  plane  to  the  other.  The  plane  (AC)  is  called  the 
normal  neutral  plane,  it  being  perpendicular  to  the  magnetic 
flux  when  there  is  no  current  in  the  armature  and,  as  a  result, 
the  field  is  not  distorted.  The  brushes  (Bj)  and  (B2)  should 
be  placed  in  this  plane,  and  when  they  are  connected  through 
an  external  circuit  there  will  be  a  current  in  the  armature 
conductors  the  value  of  which  will  depend  upon  the  value  of 
the  induced  e.m.f.  and  the  total  resistance  of  the  circuit.  The 
direction  of  this  current  in  the  inductors  will  be  the  same  as 
that  of  the  induced  e.m.f.  shown  in  Fig.  142,  and  it  will 
produce  a  certain  magnetizing  effect  upon  the  armature  core. 
This  magnetizing  effect  can  best  be  shown  by  connecting  the 
terminals  of  the  machine  to  some  source  of  e.m.f.  in  such  a 
way  that  the  current  in  the  armature  will  be  in  the  same 
direction  as  though  it  was  produced  by  the  induced  e.m.f. 
(When  the  machine  is  connected  to  the  external  source  of 
e.m.f.,  there  should  be  no  current  in  the  field  windings  and 
the  armature  should  be  stationary.)  The  magnetic  field  due 


THE  DIRECT-CUEEENT  GENEEATOR 


181 


to  the  armature  current  alone  is  shown  in  Fig.  143.  It  is 
seen  that  this  field  is  at  right  angles  to  the  field  of  the 
machine.  In  actual  operation  the  magnetizing  effect  of  the 
armature  current  and  the 
field  current  are  both 
present  at  the  same  time 
and  the  resultant  field  is 
a  combination  of  the  two 
as  shown  in  Fig.  144. 
This  results  in  a  non- 
uniform  distribution  of 
the  magnetic  flux  through 
the  generator  pole  pieces, 
air  gaps,  and  armature 
core.  The  distortion 
takes  place  in  the  direc- 
tion of  rotation  which  re- 
sults in  a  crowding  of 
the  flux  in  the  trailing 
horns  of  the  pole  pieces. 

The  neutral  plane  of  the  resultant  magnetic  field  will  make 
an  angle  with  the  normal  neutral  plane,  and  the  value  of  this 
angle  will  depend  upon  the  amount  of  armature  reaction.  As 
a  result  of  the  neutral  plane  changing  its  position,  the  posi- 
tion of  the  brushes  must  also  be  changed  so  that  it 
will  correspond  more  nearly  to  the  position  of  the 
neutral  plane.  With  a  change  in  the  position  of  the  brushes, 
there  wilj  be  a  change  in  the  direction  of  the  current  in  some 
of  the  armature  conductors.  Thus,  if  the  brushes  be  shifted 
in  the  direction  of  rotation,  as  shown  in  Fig.  145,  the  direction 
of  the  current  in  the  inductors  in  the  angle  (0)  will  change 
and  the  magnetic  effect  of  a  current  in  the  armature  will  no 
longer  be  in  a  direction  perpendicular  to  the  magnetic  field 
of  the  machine,  but  in  a  direction  such  as  that  shown  in 
Fig.  145.  This  magnetizing  effect  can  be  thought  of  as  made 
up  of  two  parts,  one  acting  parallel  to  the  magnetic  field  of 
the  machine  and  another  acting  perpendicular  to  the  magnetic 
field  of  the  machine.  The  magnetizing  effect  of  the  armature 
current  perpendicular  to  the  field  of  the  machine  is  called  the 
cross-magnetizing  effect,  and  the  effect  parallel  to  the  field  of 
the  machine  is  called  the  demagnetizing  effect.  One  of  the 


182 


PRACTICAL  APPLIED  ELECTRICITY 


above   effects   tends    to   weaken    the    magnetic    field   of   the 

machine,  while  the  other  tends  to  distort  the  magnetic  field. 

190.     Cross-Turns  and  Back  Turns. — In  the  previous  section 

it    was    pointed    out    that 

A 

•B, 


ii 


.V.j£0r:::£rx---/&^--" 


Fig.   144 


the  plane  of  the  brushes, 
known  as  the  com  mutat- 
ing plane,  should  be  moved 
in  the  direction  of  rota- 
tion in  order  that  the 
brushes  be  nearer  the  neu- 
tral plane.  The  position 
of  this  commutating  plane 
will  always  be  in  advance 
of  the  normal  neutral 
plane  in  the  case  of  a 
generator,  and  behind  the 
normal  neutral  plane  in 
the  case  of  a  motor. 

The   angle   between  the 
commutating     plane     and 

the  normal  neutral  plane  is  called  the  angle  of  lead  in  the  case 
of  a  generator,  and  the  angle  of  lag  in  the  case  of  a  motor. 
The  position  of  the  two  commutating  planes  is  shown  in 
Fig.  146,  the  full  line  (DB) 
representing  the  commu- 
tating plane  of  the  gener- 
ator and  the  dotted  line 
(FG)  representing  the 
commutating  plane  of  the 
motor.  The  conductors  in 
the  double  angle  (26)  on 
one  side  of  the  armature 
can  be  thought  of  as  being 
in  series  with  the  con- 
ductors in  the  angle  (29) 
on  the  other  side  of  the 
armature,  and  forming  a 
number  of  complete  turns 
about  the  core.  The  re- 
maining conductors  can  be  thought  of  as  forming  a  second  set 
of  turns.  The  product  of  the  turns  in  the  double  angle  (26) 


THE  DIEECT-CUEEENT  GENEEATOE 


183 


D 


and  the  current  in  them  gives  what  is  called  the  demagnetizing 
ampere-turns  because  their  effect  is  to  produce  a  weakening  of 
the  magnetic  field  of  the  machine.  The  remaining  turns  times 
the  current  in  them  are  called  the  cross-magnetizing  ampere- 
turns  because  they  act  at 
right  angles  to  the  mag- 
netic field  of  the  machines. 
The  turns  in  the  angle 
(29)  are  called  back 
turns  and  the  remaining 
ones  are  called  cross-turns. 
191.  Means  of  Reduc- 
ing Armature  Reaction. — 
Armature  reaction  inter- 
feres with  the  satisfactory 
operation  of  the  dynamo 
and  should  be  reduced  to  a 
minimum  where  possible. 
There  are  a  number  of 
ways  of  bringing  about  a 

reduction  in  the  effect  of  armature  reaction,  some  of  the  more 
important  ones  being: 

(a)  By  increasing  the  length  of  the  air  gap  of  the  machine. 

(b)  By  slotting  the  poles  parallel  to  the  axis  of  the  arma- 

ture. 

(c)  By  properly  shaping  the  pole  pieces. 

(d)  By  using  auxiliary  poles. 

(e)  By  placing  a  winding  in  perforations  in  the  pole  faces. 

(Invented  by  Mr.  Ryan.) 

(a)  Increasing   the   length   of  the   air   gap   increases   the 
reluctance  in  the  magnetic  circuit  that  is  acted  upon  by  the 
cross-magnetizing  ampere-turns,  but  at  the  same  time  increases 
the  number  of  ampere-turns  required  in  the  field  winding  of 
the  machines.    Thus  the  effect  of  the  distorting,  or  cross-turns, 
will  not  be  so  great  as  it  would  be  if  the  magnetic  field  of  the 
machine  were  weaker. 

(b)  Cutting  slots  in  the  pole  faces  parallel  to  the  axis  of 
the  armature  introduces  a  large  reluctance  in  the  path  of  the 
cross  flux,  produced  by  the  cross-magnetizing  ampere-turns, 
but  does  not  introduce  anything  like  as  great  a  reluctance  in 
the  main  magnetic  circuit.    Fig.  147  shows  a  stamping  used  in 


184 


PKACTICAL  APPLIED  ELECTRICITY 


the  construction  of  a  field  core,  there  being  a  small  slot 
punched  in  each  piece.  When  these  stampings  are  all 
assembled  there  will  be  one  long  slot  through  the  pole  piece 
parallel  to  the  axis  of  the  armature. 

(c)     The  shifting  of  the  magnetic  flux  across  the  pole  shoe 
of  the  machine  can  be  greatly  reduced  by  properly  shaping 


Fig.  147  Fig.  148 

them  so  that  the  parts  of  the  air  gap  where  the  flux  tends  to 
become  most  dense  will  have  the  greater  reluctance.  Thus  the 
pole  faces  may  be  cut  so  that  the  trailing  horn,  in  the  case  of 
a  generator,  will  be  farther  from  the  surface  of  the  armature. 
The  trailing  horn  of  the  pole  piece  may  also  be  made  longer 

than  the  advancing  side, 
which  also  results  in  a 
more  uniform  distribu- 
tion of  the  magnetic  flux 
and  the  armature  in- 
ductors will  enter  and 
leave  the  magnetic  field 
more  gradually  than  they 
would  if  an  ordinary  pole 
piece  were  used.  Such  a 
pole  piece  is  shown  in 
Fig.  148. 

(d)     Auxiliary    poles 
may  be   placed   between 
the  main  poles  of  the  ma- 
chines and  so  connected 
149  that     their     magnetizing 

effect  is  just  the  reverse  of  that  of  the  cross-magnetizing  am- 
pere-turns. The  windings  on  these  poles  are  connected  so  that 
they  carry  all  or  a  definite  portion  of  the  full  load  current. 
This  results  in  their  effect  varying  directly  as  the  load  cur- 
rent, just  as  the  effect  of  the  cross  ampere-turns  varies  with 


THE  DIRECT-CURRENT  GENERATOR 


185 


the  load  current,  and  if  the  effects  balance  for  one  particular 
load,  they  will  practically  balance  for  all  other  loads  and  the 
position  of  the  neutral  plane  of  the  magnetic  field  will  remain 
almost  constant.  The  auxiliary  poles  of  a  machine  are  shown 
in  Fig.  149. 

192.     Commutation. — The  process  of  commutation  can  best 
be  explained  by  reference  to  Fig.  150.    The  commutator  seg- 
ments are  shown  shaded  while  the  various  elements  of  the 
armature     winding     are 
shown   connected  in  series, 
the  junctions  of   these  ele- 
ments   being    connected    to 
the    commutator    segments 
in  regular  order.    The  direc- 
tion of  rotation  of  the  arma- 


ture is  indicated  by  the 
arrow  (A),  and  the  position 
of  the  neutral  plane  by  the 
line  (DE).  The  direction 
of  current  in  the  various 
elements  is  indicated  by  the  Fig.  150 

small  arrows.   With  a  direc- 
tion of  current  corresponding  to  that  shown  in  the  figure,  the 
brush  (B})  must  be  positive. 

Now  as  the  armature  rotates,  the  commutator  segments  in 
turn  pass  under  the  brush  (Bj).  If  the  contact  surface  of  the 
brush  is  greater  than  the  width  of  the  insulation  between  the 
segments,  which  should  always  be  the  case,  then  an  element 
ot  the  winding  will  be  short-circuited  when  the  brush  is  in 
contact  with  the  two  segments  to  which  the  element  is  con- 
nected. The  current  in  the  short-circuited  coil  drops  to  zero 
when  it  is  shorted,  but  it  does  not  do  so  instantly  on  account 
of  the  inductance  of  the  coil.  As  the  armature  rotates,  the 
brush  moves  from  commutator  segment  (C4),  Fig.  150,  and 
the  element  of  winding  (4)  is  connected  in  series  with 
the  other  elements  in  the  left-hand  path.  When  the  element 
becomes  a  part  of  the  left-hand  path,  it  carries  the  same 
current  the  other  elements  in  that  path  carry.  Now  if  there 
is  zero  current  in  the  coil  that  is  finishing  commutation, 
just  as  it  moves  from  the  short-circuited  position,  the  current 
in  it  must  increase  almost  instantly  to  a  value  equal  to  that 


186  PRACTICAL  APPLIED  ELECTRICITY 

in  the  other  elements.  The  inductance  of  the  element  op- 
poses this  sudden  increase  in  current  and,  as  a 'result,  there 
is  a  tendency  for  an  arc  to  form  between  the  brush  and  the 
commutator  segment  (C4)  until  the  current  in  the  coil  (4)  has 
reached  its  proper  value,  or  the  inductance  of  the  coil  has  been 
overcome.  This  condition  of  affairs  would  result  in  a  con- 
tinuous sparking  at  the  brushes,  which  would  not  only  repre- 
sent a  loss  but  would  be  injurious  to  both  the  commutator  and 
the  brushes.  Sparking  due  to  the  cause  just  mentioned  can 
be  reduced  and  practically  overcome  by  advancing  the  brushes 
beyond  the  neutral  plane.  When  the  brushes  are  thus  ad- 
vanced, there  will  be  an  e.m.f.  induced  in  the  coil  undergoing 
commutation  while  it  is  short-circuited  and  this  induced  e.m.f. 
will  be  in  such  a  direction  as  to  produce  a  current  in  the  same 
direction  as  the  current  in  the  elements  to  the  left  of  the 
brush,  as  shown  in  Fig.  150.  This  results  in  the  inductance 
of  the  coil  being  overcome  while  the  coil  is  still  short-cir- 
cuited, and  the  current  will  meet  with  no  opposition  other 
than  the  ohmic  resistance  when  the  coil  becomes  a  part  of 
the  left-hand  circuit.  Advancing  the  brushes  beyond  the 
neutral  plane  results  in  a  slight  lowering  of  the  terminal  e.m.f. 
of  the  machine,  but  this  is  more  than  offset  by  the  advantage 
in  the  reduction  in  sparking. 

193.  Capacity  of  a  Generator. — The  output  of  a  generator  is 
limited  by  one  of  the  three  following  factors,  when  sufficient 
power  is  applied  to  drive  it.  These  factors  are: 

(a)  Excessive  drop  In  the  armature  of  the  machine. 

(b)  Excessive  heating. 

(c)  Excessive  sparking. 

(a)  As  the  load  on  a  generator  is  increased,  there  is  an 
increase  in  drop  in  the  armature  due  to  the   (IR)   drop  and 
armature  reaction.     These  two  effects  combined  decrease  the 
terminal  voltage  of  the  machine  and  this  decrease  is  usually 
excessive  when  the  machine  is  overloaded. 

(b)  The  allowable  temperature  rise  as  prescribed  by  the 
American    Institute    of   Electrical   Engineers    is    as    follows: 
"Under  normal  conditions  of  operating  and  ventilation,  the 
maximum  temperature  rise  referred  to  a  standard  room  tem- 
perature of  25°  C.  should  not  exceed  50°  C.  for  field  coils  and 
armature   as   measured   by  the   increase   in   resistance;    and 
55°  C.  for  commutator  and  brushes,  and  40°  C.  for  all  other 


THE  DIKECT-CUEEENT  GENEEATOE 


187 


Field  Current 

Ffe.  151 


parts,  bearings,  etc.,  as  determined  by  a  thermometer."   It  Is 
usually  safe  to  operate  a  machine  above  these  temperatures 
for  a  few  hours,  but  an   excessive  heating  of  commutator, 
armature,  or  field  coils,  is 
likely    to    injure    and    in 
some  cases  destroy  the  in- 
sulation. 

(c)  The  heat  generated 
as  a  result  of  sparking 
usually  limits  the  allow- 
able sparking,  as  it  causes  : 
a  rise  in  temperature  of 
the  commutator  and 
the  brushes. 

194.  Building  Up  of  a 
Self-Excited  Shunt  Gener- 
ator.— The  iron  composing 
the  magnetic  circuit  of  a  generator  usually  retains  some  of  its 
magnetism  and  when  the  armature  is  revolved  in  this  weak 
magnetic  field,  there  is  a  small  e.m.f.  induced  which  produces 
a  current  in  the  field  windings.  This  current,  if  the  windings 

are  properly  connected, 
will  increase  the  magnetic 
flux  through  the  arma- 
ture, which  in  turn  will 
increase  the  e.m.f.  and 
field  current,  etc.  A  curve 
showing  the  relation  be- 
tween terminal  voltage 
and  field  current  is  given 
in  Fig.  151.  Such  a  curve 
is  called  a  magnetization 
curve.  The  abrupt  bend 
in  the  curve  near  the  top 
indicates  that  the  mag- 


Load  Current 

Fig.  152 


netic  circuit  is  practically  saturated. 

195.  External  Characteristics  of  Shunt,  Series,  and  Com- 
pound Generators. — The  external  characteristic  curve  of  a  gen- 
erator is  a  curve  that  shows  the  relation  between  the  current 
output  of  the  generator  and  the  terminal  voltage. 

In  the  case  of  the   shunt  generator,   assuming   the   speed 


188 


PEACTICAL  APPLIED  ELECTRICITY 


remains  constant  and  the  field  resistance  is  not  changed  after 
it  is  adjusted  to  give  normal  terminal  voltage  at  no  load,  the 
voltage  at  the  terminals  of  the  machine  will  decrease  with  an 
increase  in  load  on  account  of  armature  reaction  and  copper 

drop.  The  curve  in  Fig.  152 
shows  the  relation  between 
the  terminal  voltage  and 
the  load  current  for  a  shunt 
generator.  The  drop  in 
voltage  will  be  different 
for  different  machines,  de- 
pending upon  the  resist- 


ru 


•-dr 
loE 


Load  Current 

Fig.  153 


ance  of  the  armature  and 
the  amount  of  armature 
reaction. 

In  the  case  of  a  series 
generator,  the  terminal 
voltage  is  zero  with  zero 


load,  but  it  increases  as  the  load  current  increases  because 
the  field  excitation  is  increasing.  The  field  strength  of  the  ma- 
chine will  continue  to  increase  very  rapidly  with  an  increase 
in  load  until  the  iron  becomes  saturated,  when  the  effects  of 
armature  reaction  and  cop- 
per drop  produce  a  de- 
crease in  terminal  voltage 
with  a  further  increase  in 
load,  as  shown  in  Fig.  153. 
In  the  case  of  a  com- 
pound generator,  the  series 
winding  may  be  so  con- 
nected as  to  produce  a 
magnetizing  effect  that 
aids  the  shunt  field,  and 
with  an  increase  in  load 
there  is  an  increase  m 
total  field  excitation.  If 

this  increase  in  field  excitation  is  just  sufficient  to  main- 
tain the  terminal  voltage  practically  constant,  the  ma- 
chine is  said  to  be  flat-compounded.  If  there  is  a  rise  in 
terminal  voltage  with  an  increase  in  load,  the  machine  is 
said  to  be  over-compounded,  and  if  the  voltage  drops  with  an 


Load  Current 

Fig.  154 


THE  DIRECT-CURRENT  GENERATOR 


189 


increase  in  load  the  machine  is  said  to  be  under-compounded. 
The  external  characteristic  curve  of  an  over-compounded  gen- 
erator is  shown  by  curve  (A)  it,  Fig.  154,  and  the  external 
characteristic  curve  of  a  flat-compounded  generator,  by 
curve  (B). 

196.  Adaptability    of    Shunt,    Series,    and    Compound    Gen- 
erators.— The   shunt   generator  is   usually  used   where   it   is 
desired  to  have  a  practically  constant  voltage,  and  the  dis- 
tance from  the  machine  to  the  load  is  not  very  great,  resulting 
in  a  small  voltage  loss  in  the  line. 

The  series  generator  is  usually  used  in  supplying  a  constant 
current  to  a  load  at  a  varying  potential,  such  as  a  number  of 
arc  lamps  connected  in  series. 

The  compound  machine 
can  be  constructed  so  that 
the  voltage  at  its  ter- 
minals, or  at  the  load,  can 
be  maintained  constant  or 
allowed  to  increase  or  de- 
crease with  a  change  in 
load.  Thus  it  can  operate 
a  number  of  lamps  at  a 
constant  pressure  even 
though  they  be  located 
some  distance  from  the 
generator,  or  the  voltage 
at  the  end  of  the  line  can 
be  made  to  increase  with 
an  increase  of  load,  as  is 
quite  often  the  case  in 
railway  work.  A  modern  compound  generator  is  shown  in 
Fig.  155. 

197.  Losses  in  Generators.— The  losses  in  generators  may 
be  divided  into  two  main  groups: 

(A)  I2R,  or  electrical  losses. 

(B)  Stray-power  losses. 

(A)  The  I2R  losses  occur  in  the  field  windings  and  the 
armature.  If  (Ic),  (Is),  and  (Ia)  represent  the  currents  in  the 
shunt-field  winding,  series-field  winding,  and  armature,  re- 
spectively, and  (Rc),  (Rs),  and  (Ra)  represent  the  resistance 
of  the  shunt-field  winding,  series-field  winding,  and  armature, 


Fig.  155 


190  PRACTICAL  APPLIED  ELECTRICITY 

respectively,  then  the  loss  in  the  shunt-field  winding  (Wc), 
series-field  winding  (Ws),  and  armature  (Wa)  can  be  deter- 
mined by  the  following  equations: 

We  =  I2cRc  (101) 

Ws  =  I2SRS  (102) 

Wa  =  I2aRa  (103) 

(B)     The  stray-power  losses  consist  of 

(a)  Hysteresis  and  eddy-current  losses  chiefly  in  the  arma- 

ture core. 

(b)  Friction  losses  at  bearings  and  brushes,  and  air  fric- 

tion, or  windage,  as  it  is  called,  due  to  the  fan-like 

action  of  the  moving  parts. 

The  stray-power  losses  cannot  be  calculated  with  the  same 
degree  of  accuracy  that  the  (I2R)  losses  can;  but  they  can, 
however,  be  quite  accurately  determined  for  a  given  machine 
by  experiment. 

198.     Efficiency  of  Generators. — There  are  three  efficiencies 
for  a  generator: 

(a)  Efficiency  of  conversion. 

(b)  Electrical  efficiency. 

(c)  Commercial  efficiency. 

(a)  The  efficiency  of  conversion  is  the  ratio  of  the  total 
electrical    power   generated   to    the   total    mechanical    power 
supplied.     Let  (P)  represent  the  mechanical  power  supplied, 
then 

El  +  (electrical  losses) 

Efficiency  of  conversion  = X  100 

P  (104) 

Where  (El)  represents  the  output  in  watt. 

(b)  The  electrical  efficiency  is  the  ratio  of  the  total  elec- 
trical power  delivered  to  the  total  electrical  power  developed. 

El 

Electrical  efficiency  = X  100 

El  -f  (electrical  losses)  (105) 

(c)  The  commercial  efficiency  of  a  generator  is  the  ratio 
of  the  electrical  output  to  the  mechanical  input,  or 

El 

Commercial    efficiency  =    —  X  100  (106) 

P 


THE  DIRECT-CURRENT  GENERATOR  191 

The  commercial  efficiency  is  the  most  important  of  the  three, 
as  it  includes  all  the  losses  in  the  machine. 

199.  Commercial  Rating  of  Generators. — Generators  are 
rated  according  to  their  k.w.  output.  Thus  a  100-k.w.  100-volt 
generator  means  the  machine  will  deliver  100  k.w.  to  an 
external  circuit  connected  to  its  terminals,  and  that  the 
voltage  will  be  100  volts.  If  the  output  is  100  k.w.  at  100 
volts,  then  the  current  will  be  10  000  -=-  100  =  1000  amperes. 


PROBLEMS  ON   DIRECT-CURRENT  GENERATORS 

1.  Calculate  the  e.m.f.  generated  in  the  armature  of  a  10- 
pole  direct-current  generator  wound  with  1000  inductors,  lap 
winding  (simplex  singly  re-entrant),  and  revolving  at  300  revo- 
lutions per  minute.     The  magnetic  flux  per  pole  is  5  000  000 
maxwells.  Ans.     250  volts. 

2.  If  the  winding  in  the  above  problem  was  changed  to  a 
wave  winding   (simplex  singly  re-entrant),  what  e.m.f.  would 
be  generated?  Ans.     1250  volts. 

Note:  See  section  (184). 

3.  If  the  speed  in  problem  (1)  is  decreased  to  250  revolu- 
tions   per   minute   and   the   flux    (<£)    per   pole   is   raised   to 
6  000  000  maxwells,  what  would  be  the  change  in  the  e.m.f. 
generated?  Ans.     No  change. 

4.  The   armature   of   the   machine   in   problem    (1)    has   a 
resistance  of  .006  ohm,  what  will  be  the  value  of  the  terminal 
voltage   when   the   machine   is    delivering   a    current   of   750 
amperes?     (Assume  the  internal  voltage  remains  constant.) 

Ans.     245.5  volts. 

5.  How  much  should  the  flux  per  pole  be  increased  in  order 
that  the  terminal  voltage  in  problem    (4)    remain   constant? 

Ans.     Increase  90  000  maxwells. 

6.  There  are  180  inductors  on  the  surface  of  a  bipolar  drum- 
wound  armature  and  in  each  of  these  inductors  there  is  a 
current  of  50  amperes.     Calculate  the  demagnetizing  and  cross- 
magnetizing  ampere-turns  when  the  commutating  plane  makes 
an  angle  (9)  of  10  degrees  with  the  normal  neutral  plane. 

Ans.     500  demagnetizing  ampere-turns. 
4000  cross-magnetizing  ampere-turns. 


192  PRACTICAL  APPLIED  ELECTRICITY 

7.  The  total  flux  produced  by  a  field  winding  is  5  800  000 
maxwells  and  the  useful  flux  is  5  000  000  maxwells,  calculate 
the  coefficient  of  magnetic  leakage. 

Ans.     Leakage  coefficient  =  1.16. 

8.  The  output  of  a  110-volt  generator  is  300  amperes,  what 
is  the  horse-power  input  if  the  efficiency  of  the  machine  is 
90  per  cent?  Ans.     49.2  horse-power. 

9.  If  the  electrical  loss  in  problem  (8)  is  1375  watts,  what 
is  the  electrical  efficiency  of  the  machine?    The  efficiency  of 
conversion? 

Ans.    Electrical  efficiency,  96  per  cent. 

Efficiency  of  conversion,  93.8  —  per  cent. 

10.  What  is  the  commercial  efficiency  of  a  machine  that 
will  deliver  500  amperes  at  550  volts  when  the  input  is  400 
horse-power?  Ans.    92.1  +  per  cent. 


CHAPTER  X 

DIRECT-CURRENT   MOTORS 

200.  Fundamental  Principle  of  the  Direct-Current  Motor. — 
If  a  conductor  in  which  there  is  a  direct  current  be  placed  in 
a  magnetic  field  in  such  a  position  that  it  makes  an  angle  with 
the  direction  of  the  field,  there  will  be  a  force  tending  to  move 
the  conductor.     This  same  force  is  present  in  the  case  of  a 
generator,  but  it  is  overcome  by  the  mechanical  force   that 
drives  the  machine.    With  an  increase  in  current  in  the  con- 
ductor or  an  increase  in  the  strength  of  the  magnetic  field, 
there  will  be  an  increase  in  the  force  which  tends  to  move  the 
conductor. 

201.  Fleming's    Left-Hand    or    Motor    Rule. — There    is    a 
definite  relation  between  the  direction  of  current  in  a  con- 
ductor, the  direction  of  motion,  and  the  direction  of  the  mag- 
netic field  for  a  motor;   just  as  there  is  a  definite  relation 
between  these  three  quantities  in  the  case  of  a  generator.    If 
the  thumb  and  first  and  second  fingers  of  the  left  hand  be 
placed  at  right  angles  to  each  other,  the  second  finger  pointing 
in  the  direction  of  the  current  in  the  conductor,  the  first  finger 
in  the  direction  of  the  magnetic  field,  then  the  thumb  will 
point  in  the  direction  in   which  the  conductor  will  tend   to 
move.     This  simple  rule  is  known  as  Fleming's  left-hand  or 
motor  rule.     If  the  direction  of  the  current  in  the  conductor 
be   reversed,  the  direction  of  the   magnetic   field  remaining 
constant,  the  direction  of  motion  will  be  reversed;  or,  if  the 
direction  of  the  magnetic  field  be  reversed,  the  direction  of 
the  current  remaining  the  same,  the  direction  of  motion  will 
be  reversed.     If,  however,  the  direction  of  the  current  and 
the  direction  of  the  magnetic   field   are  both  reversed,   the 
direction  of  motion  of  the  conductor  will  remain  the  same. 
Fig.  156  illustrates  Fleming's  left-hand  rule. 

202.  Generator  and  Motor  Interchangeable. — The  essential 
parts  of  a  direct-current  motor  are  identical  with  those  of  a 

193 


194  PEACTICAL  APPLIED  ELECTRICITY 

generator,  namely,  an  armature  and  magnetic  field.    The  con- 
nection of  the  armature  conductors  to  the  external  circuit  is 
made  by  means  of  a  commutator  which  serves  to  reverse  the 
direction    of    current    in    the    armature 
winding  at  the  proper  time  so  that  the 
forces  tending  to  move  the  various  con- 
ductors in  the  magnetic  field  all  act  to- 
gether and  a  continuous  rotation  of  the 
armature  is  produced.  Any  direct-current 
etic        generator  may  be  used  as  a  direct-cur- 

rent    mOtOI>    Or   vice    Versd>    their    COnstrUC- 

tion  being  practically  the  same. 
Fig.  156  203.      Classes    of    Motors.  —  Direct-cur- 

rent motors  may   be   divided   into  three 

main  groups  according  to  the  method  employed  in  exciting 

the  field  magnets.    These  are: 

(a)  Shunt  motors. 

(b)  Series  motors. 

(c)  Compound  motors. 

(a)  The  field  windings  of  a  shunt  motor  consist  of  a  large 
number  of  turns  of  small  wire  connected  directly  across  the 
terminals  of  the  machine,  or  the  line  to  which  the  machine  is 
connected.     The   current   in   the   field   winding   of   a   shunt 
machine  is  independent  of  the   current  in  the  armature  so 
long  as  an  increase  in  armature  current  produces  no  change 
in  the  voltage  impressed  upon  the  shunt  field  winding.     The 
field  strength  of  the  shunt  machine  is  regulated  by  changing 
the  current  in  the  field  winding,  which  may  be  done  by  either 
changing  the  impressed  voltage  or  the  total  resistance  of  the 
circuit. 

(b)  In  the  case  of  the  series  motor,  the  field  winding  con- 
sists of  a  few  turns  of  large  wire  connected  directly  in  series 
with  the  armature  and  the  line.     The   current  in  the  field 
windings  is  the  same  as  the  current  in  the  armature,  and  the 
^eld  strength  varies  with  the  load  on  the  machine,  the  field 
current  increasing  with  the  load. 

(c)  The  field  windings  of  a  compound  motor  are  a  combi- 
nation of  the  shunt  and  the  series  windings.     The  magnetic 
effect  of  these  two  windings  may  aid  or  oppose  each  other,  de- 
pending upon  the  way  they  are  connected.     When  the  two 
magnetizing  effects  act  together,  the  machine  is  called  a  cumu- 


DIRECT-CURRENT  MOTORS 


195 


lative  compound  motor;  and  when  their  magnetizing  effects 
oppose  each  other,  the  machine  is  called  a  differential  com- 
pound motor.  In  the  case  of  the  cumulative  compound 
machine,  the  field  strength  increases  with  an  increase  in  load 
I  since  the  two  magnetizing  effects  act  together;  and  in  the 
case  of  the  differential  compound  motor,  the  field  strength 
decreases  with  an  increase  in  load  since  the  two  magnetizing 
effects  act  opposite  to  each  other. 

204.  Direction  of  Rotation  of  Machines  when  Changed  from 
a  Generator  to  a  Motor. — The  direction  of  current  in  the 
armature,  field  winding,  and  line  for  a  self-excited  shunt 
generator,  and  the  polarity  of  the  machine  and  direction 

To  Line 


Fig-.  157 


Fig.  158 


of  rotation  are  shown  in  Fig.  157.  The  arrow  (Ia)  repre- 
sents the  direction  of  the  armature  current.  Let  this  ma- 
chine be  operated  as  a  motor  by  connecting  it  to  some 
source  of  energy,  connecting  the  positive  terminal  of  the 
machine  to  the  positive  line,  and  the  negative  terminal  of 
the  machine  to  the  negative  line.  The  direction  of  current 
in  the  field  and  armature  for  this  connection  is  shown  in 
Fig.  158.  It  will  be  seen  by  inspection  that  the  direction  of 
current  in  the  field  winding  has  remained  the  same  in  the  two 
cases  and  that  the  direction  of  current  in  the  armature  has 
changed.  Now  applying  Fleming's  dynamo  rule  to  Fig.  157 
and  his  motor  rule  to  Fig.  158 — remembering  the  direction  of 
current  in  the  armature  in  one  case  is  just  the  reverse  of 
what  it  is  in  the  other,  and  the  field  current  is  the  same  in 
both  cases — you  will  find  the  direction  of  rotation  of  the  arma- 
ture in  Fig.  158  will  be  the  same  as  in  Fig.  157. 

In  the  change  from  a  generator  to  a  motor,  as  shown  in 
Figs.  157  and  158,  the  polarity  of  the  terminals  of  the  motor 
was  the  same  as  that  of  the  generator.  When  the  polarity  of 


PRACTICAL  APPLIED  ELECTRICITY 

the  motor  is  just  the  reverse  of  that  of  the  generator,  the 
current  in  the  shunt-field  winding  will  be  reversed  in  direc- 
tion and  the  armature  current  will  not  change.  This  will  also 
result  in  the  direction  of  rotation  of  the  armature  remaining 
the  same.  Hence,  a  shunt  generator  will  always  run  in  the 
same  direction  when  operated  as  a  motor,  as  it  did  when  it 
was  run  as  a  generator. 

To  change  the  direction  of  rotation  of  a  shunt  generator 
when  it  is  changed  to  a  motor,  the  connections  of  the  arma- 
ture or  shunt-field  winding  must  be  reversed. 

When  a  series  generator  is  changed  to  a  series  motor,  the 
direction  of  rotation  will  be  reversed,  because  the  direction  of 
the  current  in  the  field  winding  and  the  armature  bear  the 
same  relation  to  each  other  in  both  cases  and  the  motion  will 
be  opposite  as  shown  by  the  right-  and  left-hand  rules.  Chang- 
ing the  connection  of  the  machine  to  the  line  will  not  change 
the  direction  of  rotation  as  the  current  in  both  the  armature 
and  field  winding  is  reversed  when  such  a  change  is  made. 
Then  in  order  to  change  the  direction  of  rotation  of  the 
armature,  the  connections  of  either  the  series  field  winding 
or  armature  must  be  reversed,  which  will  result  in  a  change 
in  direction  of  either  the  magnetic  field  or  of  the  armature 
current,  but  not  of  both. 

The  compound  generator  will  act,  as  far  as  direction  of 
rotation  is  concerned,  when  changed  to  a  motor,  the  same  as 
though  it  were  a  simple  shunt  machine,  provided  the  machine 
is  lightly  loaded.  If  it  is  started  under  a  heavy  load  there 
will  be  an  excessive  current  in  the  armature  and  series-field 
winding,  and  if  the  magnetizing  effect  of  the  series-field 
winding  is  greater  than  that  of  the  shunt-field  winding,  the 
machine  will  start  up  as  though  it  were  a  series  motor. 

205.  Armature  Reaction  in  a  Motor. — Let  us  assume  that  a 
shunt  generator  is  operated  as  a  shunt  motor,  the  polarity  of 
the  machine  being  the  same  in  both  cases.  The  current  in 
the  shunt-field  winding  will  remain  constant  in  direction  and, 
as  a  result,  the  direction  of  the  magnetic  field  of  the  machine 
does  not  change.  The  direction  of  current  in  the  armature, 
however,  changes  and  as  a  result  the  direction  of  the  magnetic 
field  produced  by  it  changes.  When  the  brushes  are  in  the 
normal  neutral  plane,  as  shown  in  Fig.  143,  the  field  produced 
by  the  armature  current  is  at  right  angles  to  that  produced  by 


DIEECT-CUEEENT  MOTOES 


197 


the  field  current  and  it  is  acting  downward,  as  shown  in  Fig. 
159,  instead  of  upward,  as  shown  in  Fig.  143.  Since  the  mag- 
netizing effects  of  the  armature  current  and  the  field  current 
are  present  at  the  same 
time,  they  form  a  resultant 
field  whose  general  direc- 
tion is  similar  to  that 
shown  in  Fig.  160.  It  will 
be  seen  that  the  magnetic 
field  in  the  case  of  a  motor 
is  shifted  in  a  direction  op- 
posite to  the  direction  of 
rotation,  which  is  just  the 
reverse  of  what  occurred 
in  the  generator,  as  shown 
in  Fig.  144.  This  results 
in  the  neutral  plane  of  the 
magnetic  field  being  shift- 
ed back  of  the  normal 
neutral  plane,  as  shown  by  the  line  (FG)  in  Fig.  160. 

206.  Position  of  the  Brushes  on  a  Motor. — Since  the  neutral 
plane  of  the  magnetic  field  is  changed  when  the  generator  is 
changed  to  a  motor,  the  plane  in  which  the  brushes  are  placed 

must  be  changed   so  that 
p  it    will    correspond    more 

A      B(>/  nearly  to   the  position  of 

the  neutral  plane.  The 
brushes  then  will  be  given 
an  angle  of  lag  in  the  case 
of  a  motor  while  they  were 
given  an  angle  of  lead  in 
the  case  of  a  generator. 

The  demagnetizing  turns 
on  the  armature  are  in  the 
angle    (26),   as    shown   in 
Fig.    146,    and    the    cross- 
magnetizing  turns  are those 
outside  of  this  double  an- 
gle.   The  turns  in  the  dou- 
ble angle   (26)   are  still  demagnetizing,  although  the  current 
through  the   armature  has  been  reversed,   for  the  following 


198  PEACT1CAL  APPLIED  ELECTEICITY 

reason:  When  the  machine  is  used  as  a  generator  the  brushes 
are  in  advance  of  the  neutral  plane,  as  shown  in  Fig.  145, 
and  when  it  is  used  as  a  motor  they  are  back  of  the  neutral 
plane,  as  shown  in  Fig.  160.  If  the  brushes  were  changed  from 
one  position  to  the  other  without  reversing  the  current  in  the 
armature,  the  current  in  the  turns  located  in  the  angle  (20) 
would  be  reversed  in  direction  and  the  magnetizing  effect  of 
the  ampere-turns  in  this  angle  (20)  would  act  with  the  mag- 
netic field  of  the  machine.  The  current  in  the  armature,  how- 
ever, is  reversed  at  the  same  time  the  position  of  the  brushes 
is  changed  and,  as  a  result,  the  magnetizing  effect  of  the 
turns  in  the  angle  (20)  does  not  change  in  direction. 

The  brushes  are  usually  placed  a  little  back  of  the  neutral 
plane  in  the  case  of  a  motor  for  the  same  reason  they  are 
placed  in  advance  of  the  neutral  plane  in  the  case  of  a 
generator,  as  explained  in  section  (192). 

207.  Torque  Exerted  on  Armature. — The  torque  of  a  motor 
is  equal  to  the  product  of  the  total  force  acting  on  the  arma- 
ture conductors  times  the  distance  of  the  conductors  from  the 
center  of  the  armature,  or 

T  =  F  X  L-  (107) 

•  ••  ' 
When  the  force   (F)   in  the  above  equation  is  measured  in 

pounds  and  the  distance  (L)  between  the  point  of  application 
of  this  force  and  the  center  of  the  armature  is  measured  in 
feet,  the  torque  (T)  will  be  given  in  pound-feet.  The  follow- 
ing equation  can  be  used  in  calculating  the  torque  in  pound- 
feet  in  terms  of  the  total  number  of  conductors  (Z)  on  the 
armature,  the  number  of  poles  (p),  the  magnetic  flux  per  pole 
(3>),the  number  of  paths  in  parallel  through  the  armature  (b), 
and  the  total  armature  current  (Ia). 

.1174  XpXZx$Xla 

T  = (108) 

108  X  b 

208.  Mechanical  Output  of  a  Motor. — The  output  of  a  motor 
in  foot-pounds  per  second  is  equal  to  the  torque  (T)  in  pound- 
feet  multiplied  by  the  speed  in  revolutions  per  second  (r.p.s.) 
times  2  ?r.     Since  one  horse-power  is  equal  to  550  foot-pounds 
per  second,  then  the  output  of  a  motor  in  horse-power  (h.p.) 
can  be  calculated  by  the  use  of  the  following  equation: 


DIRECT-CURRENT  MOTORS  199 

27r  X  T  X  (r.p.s.) 

h.p.  =  (109) 

550 

If  the  speed  is  measured  in  revolutions  per  minute   (r.p.m.), 
then 

27T  X  T  X  (r.p.m.) 

h.p.=  (110) 

33000 

209.  Counter    Electromotive    Force. — When   a   machine   is 
being  operated  as  a  motor,  the  armature  is  revolving  in  a 
magnetic  field  and  there  will  be  an  induced  e.m.f.  set  up  in 
the  conductors  just  the  same  as  there  would  be  if  the  machine 
were  operated  as  a  generator.     Since  the  relation  between 
the  direction  of  motion  of  the  conductors  with  respect  to  the 
direction  of   the   magnetic   field   in   the   case   of  a  motor   is 
opposite  to  what  it  is  in  the  case  of  a  generator,  the  direction 
of  the   current   in   the   conductors    remaining   constant,   the 
induced  e.m.f.  in  the  armature  of  the  motor  will  be  just  the 
reverse  of  what  it  is  in  the  case  of  the  generator.    This  e.m.f. 
opposes  the  flow  of  the  electricity  in  the  armature  and  hence 
takes  energy  from  it,  just  as  a  force  that  acts  in  a  direction 
opposite  to  the  velocity  of  a  body  takes  energy  from  the  body, 
hence  the  motor  action.     This  induced  e.m.f.  acts  in  a  direc- 
tion just  opposite  to  the  impressed  e.m.f.  at  the  terminals 
of  the  machine  and  for  that  reason  it  is   called  a  counter 
electromotive  force.    Its  value  depends  upon  the  same  factors 
as  the  e.m.f.  of  a  generator,  and  it  may  be  calculated  by  the 
use  of  equation  (100).     A  counter  e.m.f.  is  absolutely  neces- 
sary to  the  operation  of  a  motor. 

210.  Normal  Speed  of  a  Motor. — The  current  in  the  arma- 
ture of  a  motor  depends  upon  the  resistance  of  the  circuit, 
and  the  effective  electromotive  force  acting  in  the  circuit.     If 
the  impressed  voltage  on  the  machine  be  represented  by  (E), 
the   counter  electromotive  force  by    (Ec),  and  the  effective 
electromotive  force  by  (Ef),  then 

Ef  =  E  — EC  (111) 

The  current  (In)  in  the  armature  is  equal  to 

Er 

Ia  =  -  (112) 

R, 


200  PBACTICAL  APPLIED  ELECTRICITY 

or 

E  —  EC 


(113) 


Ra 


In  the  above  equations  (Ra)  represents  the  total  resistance 
between  the  terminals  of  the  machine,  neglecting  the  shunt 
field.  In  a  shunt  machine  (Ra)  would  be  the  resistance  of  the 
armature,  while  in  a  series  and  compound  machine  (Ra)  would 
be  the  resistance  of  the  series  field  and  armature  combined. 
Since  the  current  is  dependent  upon  the  counter  electromotive 
force,  as  shown  in  equation  (113),  the  machine  will  run  at 
such  a  speed  that  the  difference  between  the  impressed  voltage 
(E)  and  the  counter  electromotive  force  will  produce  suf- 
ficient current  in  the  armature  to  produce  the  required  torque 
in  order  that  the  machine  may  carry  its  load.  Thus,  with  an 
increase  in  load  on  a  machine  there  will  be  an  increase  in 
torque  required,  and  this  increase  in  torque  will  mean  an 
increase  in  armature  current  if  the  field  strength  remains 
constant.  Now  in  order  that  the  current  in  the  armature 
increase,  the  resistance  (Ra)  and  impressed  voltage  (E) 
remaining  constant,  the  value  of  the  counter  e.m.f.  must 
decrease.  The  only  factor  in  equation  (100)  that  can  change 
is  the  speed,  since  the  field  strength,  or  flux  per  pole  (<£),  is 
supposed  to  remain  constant  and  the  other  factors  are  gov- 
erned by  the  construction  of  the  machine  and  cannot  be 
changed  without  rebuilding.  There  will  then  be  a  reduction 
in  the  speed  of  a  machine  with  an  increase  in  load  current, 
all  other  factors  remaining  constant. 

211.  Methods  of  Regulating  the  Speed  of  a  Motor. — The 
speed  of  a  motor  may  be  regulated  by  any  one,  or  certain 
combinations  of  the  following  methods: 

(a)  Change  in  field  strength  produced  by  a  change  in  field 

current. 

(b)  Change  in  field  strength  produced  by  a  change  in  the 

reluctance  of  the  magnetic  circuit. 

(c)  Varying  voltage   over  the   armature   by   means   of  a 

rheostat. 

(d)  Multi-voltage  system. 

(e)  By  changing  the  position  of  the  brushes. 

(a)     A  rheostat  placed  in  series  with  the  shunt  field  of  a 


DIRECT-CURRENT  MOTORS 


201 


Fig.  161 


motor,  as  shown  in  Fig.  161,  may  be  used  to  change  its  speed. 
If  the  resistance  of  the  shunt-field  circuit  be  increased  by 
increasing  the  part  of  the  resistance  (R)  in  circuit,  the  field 
current  will  be  decreased  and  there  will  be  a  decrease  in  the 
magnetic  flux  (<£)  per  pole  which 
will  result  in  an  increase  in  speed, 
all  other  quantities  remaining  con- 
stant, in  order  that  the  required 
counter  e.m.f.  may  be  generated  in 
the  armature.  The  change  in  the 
value  of  (<t>)  due  to  a  change  in  the 
field  current  will  depend  upon  the 

degree  to  which  the  iron  of  the  magnetic  circuit  of  the  ma- 
chine is  saturated.  If  the  circuit  is  well  saturated  there  must 
be  a  relatively  large  change  in  field  current  to  produce  a 
small  change  in  speed. 

There  is  a  limit,  however,  to  the  amount  you  can  weaken 
the  field  of  a  machine  as  the  armature  reaction  increases  with 
a  decrease  in  field  strength  which  results  in  serious  sparking. 
The  effect  of  armature  reaction  can  be  neutralized  as  ex- 
plained in  section  (191)  and  the  allowable  range  in  speed  ob- 
tainable by  this  method  thus  greatly  increased.  A  number* 
of  different  kinds  of  field  rheostats  are  described  in  the  chap- 
ter on  operation. 

(b)  The  magnetic  flux 
in  the  magnetic  circuit  of 
a  machine  can  be  changed 
by  varying  the  reluctance 

V  *J    !§  v"'""v        of    the    magnetic    circuit. 

JT  T  Field  This  is  accomplished  in  the 
case  of  a  motor  manufac- 
tured by  the  Stow  Manu- 


162 


facturing  Company,  in  the 

following  way:  The  field  cores  are  hollow  and  are  provided 
with  movable  iron  cores.  These  cores  are  all  connected 
mechanically  so  that  their  position  in  the  field  coils  can  be 
adjusted  by  means  of  a  hand  wheel  on  top  of  the  machine. 
By  moving  them  toward  or  away  from  the  armature  there  will 
be  a  decrease  or  increase  in  the  reluctance  of  the  magnetic 
circuit  and,  as  a  result,  an  increase  or  decrease  in  the  flux  ($) 
per  pole.  This  change  in  (3>)  will  produce  a  change  in  the  speed. 


202  PEACTICAL  APPLIED  ELECTKICITY 


(c)  If  a  rheostat  (Ri)  be  placed  in  series  with  the  armature 
of  a  motor,  as  shown  in  Fig.  162,  the  voltage  across  the 
terminals  of  the  armature  circuit  can  be  varied  by  changing 
the  resistance  in  the  rheostat.  A  change  in  impressed  voltage 
on  the  armature  will  mean  a  change  in  speed,  because  there 
will  be  a  change  in  the  value  of  the  counter  e.m.f.  required. 
The  Ward  Leonard  system,  as  described  in  section  (213),  is  a 
form  of  variable  voltage  control. 

(d)      In  the  multi-voltage  method 

fs/|ajn  A  of  speed  control,  there  are  several 

~T"         different     voltages     available     from 

Main  J3 a4oVolt5      which  the  motor  may  be  operated. 

.    r         ^Volts  Thus,  as  shown  in  Fig.  163,  there  is 

a  different  voltage  between  the  dif- 


Ma,nD64ltsl 


ferent  lines  and  these  may  be  com- 
bined, giving  other  voltages,  which 
Fig.  163  may  be  connected  to  the  motor  ter- 

minals by  means  of  a  suitable  switch, 

or  controller.     This  method  is  usually  used  in  combination 

with  the  field  rheostat  method. 

(e)  If  the  brushes  of  a  machine  be  shifted  from  the  neutral 
plane  of  the  magnetic  field,  there  will  be  an  increase  in  the 
speed  for  the  following  reason:  The  counter  e.m.f.  between 
the  brushes  of  a  motor  is  a  maximum  when  the  brushes  are  in 
the  neutral  plane  because  the  e.m.f.  induced  in  all  the  con- 
ductors, in  series  in  the  various  paths  through  the  armature 
windings,  are  acting  in  the  same  direction.  If  the  position  of 
the  brushes  be  changed,  it.  will  result  in  the  e.m.f.  induced  in 
some  of  the  conductors  in  series  opposing  the  e.m.f.  in  the 
others;  and  the  resultant  e.m.f.  will  be  less  than  in  the  pre- 
vious case,  all  other  conditions  remaining  constant.  Now  as 
the  brushes  are  shifted  from  the  neutral  plane,  the  speed  must 
increase  in  order  that  the  counter  e.m.f.  between  the  brushes 
may  satisfy  equation  (113).  This  is  not  a  practical  method  for 
varying  the  speed,  as  excessive  sparking  usually  results  when 
the  brushes  are  moved  very  much  from  their  proper  position. 
The  brushes,  in  the  case  of  a  motor,  can  be  placed  in  the 
neutral  plane  by  moving  them  back  and  forth,  noting  the 
change  in  speed.  The  position  giving  a  minimum  speed  will 
correspond  to  the  neutral  plane  (no  load  on  the  motor). 


DIRECT-CURRENT  MOTORS 


203 


212.  Inter  pole   Motor. — In  order  to  prevent  a  shift  in  the 
position  of  the  neutral  plane  of  the  magnetic  field  of  a  motor, 
due  to  a  change  in  armature  current,  which  tends  to  distort 
the  field,  commutating-poles,  or  interpoles,  are  used.     These 
poles  are  placed  between  the  regular  poles  of  the  machine, 
and  the  windings  on  them  carry  the  load  current.    Their  mag- 
netizing effect  counteracts  that  of  the  armature  current  and 
the  position  of  the  brushes  need  not  be  changed  with  the 
change  in  load  on  the  machine.    If  the  direction  of  rotation  of 
the  armature  be  changed  by  changing  the  direction  of  the 
armature  current,  the  polarity  of  the  interpoles  will  also  be 
changed  and  their  magnetizing  effect  will  still  counteract  that 
of  the  armature  current. 

213.  Ward    Leonard   System. — In  this  system   the   field  of 
the  motor  (M)  is  connected  directly  to  the  main  line  and  the 


Fig.  164 

armature  is  connected  to  an  auxiliary  generator  (G),  whose 
voltage  can  be  regulated  by  means  of  the  field  rheostat  (R), 
Fig.  164.  In  this  arrangement  the  speed  of  the  motor  (M)  is 
controlled  by  a  change  in  impressed  voltage,  which  in  turn 
is  controlled  by  the  excitation  of  the  generator  (G).  The 
field  current  for'  the  generator  (G)  is  taken  directly  from 
the  line  and  its  value  is  regulated  by  means  of  the  rheo- 
stat (R). 

214.  Comparison  of  Methods  of  Speed  Control. — The  field 
rheostat  method  is  perhaps  the  cheapest  and  simplest  method 
of  speed  control  and  for  that  reason  is  no  doubt  used  more 
than  any  of  the  others.  It  permits  of  a  wide  variation  in 
speed  when  used  with  the  interpole  motor  and  the  change 
in  the  speed  can  be  made  very  gradually. 

The  change  in  reluctance  method  is  quite  satisfactory,  but 


£04  PRACTICAL  APPLIED  ELECTRICITY 

the  initial  cost  of  the  machine  is  usually  prohibitive  for 
.general  use. 

The  armature  rheostat  method  is  very  little  used,  as  there 
is  a  large  change  in  speed,  with  a  change  in  load,  and  there 
is  an  excessive  loss  in  the  resistance  for  large  armature  cur- 
rents. 

The  Ward  Leonard  and  multi-voltage  systems  are  very  sat- 
isfactory in  operation,  but  they  are  expensive  to  install. 

A  change  in  speed  produced  by  shifting  the  brushes  is 
not  practical  on  account  of  difficulties  due  to  sparking. 

215.  Starting  Motors. — There  is  no  counter  e.m.f.  generated 
in  the  armature  of  a  motor  when  it  is  stationary  and  if  the 
machine  were  connected  directly  to  line  a  very  destructive 
current  would  exist  in  the  armature.  The  value  of  this  cur- 
rent, just  at  the  instant  the  circuit  was  closed,  would  be 
equal  to  (E)  divided  by  (Ra)  if  there  were  no  resistance 
in  series  with  the  armature.  The  resistance  of  the  arma- 
ture is  usually  very  small  and,  as  a  result,  the  current  would 
be  large.  By  placing  a  resistance  (Rx)  in  series  with  the 
armature,  the  current  can  be  reduced  to  a  safe  value.  Now 
as  the  armature  starts  to  rotate  there  will  be  a  counter 
e.m.f.  generated  and  the  effective  e.m.f.  acting  in  the  circuit 
will  be  reduced,  which  will  cause  a  reduction  in  current,  and 
the  speed  will  become  constant  in  value  when  the  effective 
e.m.f.  acting  in  the  circuit  is  equal  to  the  product  of  the 
current  and  the  total  resistance,  or 

E  —  EC  =  L  (Ra  +  Rx)  (114) 

In  the  above  equation  (Ra)  represents  the  resistance  of  the 
armature  and  <RX)  the  resistance  connected  in  series  with 
the  armature.  If  the  resistance  (Rx)  be  decreased,  there 
must  be  an  increase  in  speed,  the  armature  current  (In)  re- 
maining practically  constant,  in  order  that  the  effective  e.m.f. 
(E  —  EC)  will  be  equal  to  the  (IaR)  drop  in  the  armature 
circuit.  When  all  of  the  resistance  (Rx)  is  cut  out  of  the 
circuit,  the  effective  e.m.f.  is  equal  to  the  armature  current 
(Ia)  times  the  armature  resistance,  or 

E  — Ec  =  IaRa  (115) 

and 

E  — EC 
Ia  =  -  (116) 

Ra 


DIRECT-CURRENT  MOTORS 


205 


Supply 
Mains 


The  field  circuit  of  the  motor  must,  of  course,  be  closed  .when 
it  is  being  started  in  order  that  the  armature  conductors 
may  cut  lines  of  force  and  have  a  counter  e.m.f.  induced 
in  them,  and  also  that  the  proper  torque  be  generated  to 
cause  the  armature  to  rotate. 

216.      Starting    Boxes,    or     , 

Rheostats. —  A  resistance 
that  can  be  connected  in 
the  circuit  leading  to  the 
motor  and  so  constructed 
that  it  may  be  slowly  cut 
out  as  the  motor  speeds  up, 
is  called  a  starting  box,  or 
starting  rheostat.  A  simple 
starting  rheostat  is  shown 
in  Fig.  165.  The  shunt  field 
is  connected  directly  to  the 
supply  mains  and  the  arma- 
ture is  connected  through 
the  resistance  (Rx).  When 


Fig.  165 


the  switch  (S)  is  first  closed,  all  of  the  resistance  (Rx) 
should  be  in  circuit  and  as  the  motor  speeds  up,  it  may  be 
gradually  reduced  and  finally  all  cut  out. 

217.  Dead-Line  Release. — In  the  operation  of  a  shunt  motor, 
as  shown  in  Fig.  165,  the  armature  may  be  destroyed  by  an 
excessive  current  resulting  from  the  line  becoming  dead  for 
a  short  time,  which  results  in  the  speed  of  the  motor  decreas- 
ing immediately,  and  when  the  full  line  voltage  is  again  ap- 
plied the  counter  e.m.f.,  on  account  of  the  decrease  in  speed, 
will  not  be  of  sufficient  value  to  prevent  an  excessive  cur- 
rent in  the  armature.  To  prevent  the  above  condition  oc- 
curring, the  starting  box  can  be  provided  with  what  is  called 
a  no-voltage  or  dead-line  release  magnet,  as  shown  in  Fig. 
166.  The  winding  of  this  magnet  may  be  connected  in 
series  with  the  shunt  field  winding,  as  shown  in  the  figure; 
however,  in  adjustable  speed  motors,  it  is  usually  con- 
nected directly  across  the  line.  The  arm  (A)  is  moved 
from  its  initial  position  against  the  action  of  a  coil  spring 
and  it  is  held  in  the  extreme  right-hand  position  by  the 
magnet  (M).  If  the  current  in  the  winding  of  (M)  be  reduced 
to  such  a  value  that  the  magnet  will  no  longer  hold  the  arm 


206 


PRACTICAL  APPLIED  ELECTRICITY 


(A),  the  arm  will  be  released  and  it  will  return  to  its  initial 
position.  This  will  result  in  the  armature  and  field  circuits 
both  being  opened  if  the  line  to  which  the  motor  is  connected 
should  become  dead.  The  arm  (A)  must  then  be  moved  by 
an  attendant  to  its  right-hand  position  in  order  to  operate  the 
motor  when  the  line  becomes  alive. 

218.  Overload  Release.— 
The  armature  of  a  motor 
may  be  burned  out,  due  to 
an  excessive  current  pro- 
duced by  the  motor  being 
overloaded,  and  the  purpose 
of  the  overload  release  is  to 
open  the  circuit  or  discon- 
nect the  motor  from  the 
lire  before  the  machine  is 
injured,  due  to  an  excessive 
current.  The  overload  re- 
lease magnet  winding  car- 
ries the  armature  current 
and  when  this  becomes  ex- 
cessive a  piece  of  iron  is 
attracted,  which  shorts  the 
no-voltage  release  magnet 
and  allows  the  arm  to  re- 
turn to  its  initial  position. 

A  starting  box  equipped  with  an  overload  release  is  shown 
in  Fig.  167. 

219.  Combined  Starting  and   Field-Regulating   Rheostats. — 
In   a    rheostat   of   this   kind    a    field-regulating   resistance    is 
combined  with  a  starting  box.     Such  a  rheostat  as  manufac- 
tured   by    the    Cutler-Hammer    Manufacturing    Company    is 
shown  in  Fig.  168.     The  movable  arm  consists  of  two  parts 
and  their  outer  ends  move  over  separate  sets   of  contacts. 
When  the  motor  is  being  started,  the  arm  is  moved  to  the 
extreme  right-hand   position   and  the   lower   portion   is   held 
there  by  the  no-voltage  release  magnet,  while  the  upper  por- 
tion may  then  be  moved  back  over  the  upper  row  of  contacts 
which   are   connected   to   the   field-regulating   resistance.     A 
diagram  of  this  starting  box  is  shown  in  Fig.  169. 

220.  Speed   Regulation. — The  speed  regulation  of  a  motor 


Fig.  166 


DIRECT-CUEEENT  MOTOES 


207 


is  the  change  in  speed  from  full  load  to  no .  load  expressed 
as  a  percentage  of  the  full  load  speed,  the  field  resistance 
and  impressed  voltage  remaining  constant.  Thus,  if  the 
speed  of  a  shunt  motor  is  1000  r.p.m.  at  full  load  and  1050 
r.p.m.  at  no  load,  its  speed  regulation  is 
1050  — 1000 

-  X  100  =  5  per  cent 
1000 

In  order  that  the  speed  of  the  machine  may  remain  constant 
with  a  change  in  load  the  field  strength  of  the  machine  must 
be  changed. 

Characteristics  of  the  Shunt 
Motor. — The  change  in  torque, 
current,  and  speed  that  takes 
place  as  the  load  on  a  shunt 
motor  changes  is  shown  in  Fig. 
170.  There  is  a  decrease  in 
speed  with  an  increase  in  load. 
The  current  and  torque  both  in- 
crease at  about  the  same  rate, 
with  an  increase  in  load,  since 
the  field  strength  remains  prac- 
tically constant. 

221.  Characteristics  of  the  Se- 
ries Motor. — The  speed  of  a 
series  motor  will  drop  off  a 
great  deal  more  with  an  increase 

in  load  than  in  the  case  of  a  shunt  motor  because  there  is 
an  increase  in  field  strength  with  an  increase  in  load.  Care 
should  be  taken  in  the  operation  of  series  motors  to  see  that 
their  load  never  drops  to  zero  while  they  are  connected  to 
the  source  of  energy,  as  their  speed  will  become  excessive 
or  they  will  "race."  If  the  iron  of  the  magnetic  circuit  is 
worked  near  saturation  or  above  the  "knee"  of  the  mag- 
netization curve,  the  change  in  speed  will  not  be  as  great 
as  it  is  when  the  iron  is  not  so  near  saturation.  The  in- 
crease in  torque  with  an  increase  in  load  must  necessarily 
be  greater  than  in  the  case  of  a  shunt  motor,  as  the  decrease 
in  speed  is  greater.  The  torque  is  proportional  to  the  arma- 
ture current  and  field  strength,  and  the  field  strength  varies 
almost  directly  a?  the  armature  current,  the  series  winding 


Fig.  167 


208 


PBACTICAL  APPLIED  ELECTRICITY 


and  armature  being  connected  in  series.  If  the  iron  is  be- 
low the  knee  of  the  magnetization  curve  the  torque  will 
then  vary  practically  as  the  square  of  the  current;  when, 
however,  the  magnetic  circuit  is  worked  above  the  knee  of 
the  curve,  the  variation  in  torque  due  to  a  change  in  current 
becomes  less.  The  change  in  torque,  current,  and  speed  that 
takes  place  as  the  load  on  a  series  motor  changes,  is  shown 

in  Fig.  171. 

222.  Characteristics 
of  the  Compound  Motor. 
When  the  compound 
motor  is  connected  so 
its  two  fields  aid  each 
other,  its  characteristics 
are  between  those  of 
the  shunt  and  the  series 
motor.  If  the  magnet- 
izing action  of  the  se- 
ries field  opposes  that 
of  the  shunt  field,  the 
speed  remains  nearer 
constant  with  an  in- 
crease in  load  than  it 
does  for  a  shunt  motor. 
The  torque  does  not 

need  to  increase  so  rapidly  as  a  result  of  the  speed  remaining 
constant,  as  it  does  in  the  case  of  a  shunt  motor.  The  arma- 
ture current  must  increase,  since  the  field  strength  is  de- 
creased in  order  that  the  same  torque  be  produced  in  the  case 
of  a  shunt  and  differential  compound  motor. 

223.  Adaptability  of  Different  Motors.— There  are  three 
different  classes  of  work  to  be  performed  by  motors,  each 
requiring  a  different  relation  between  motor  torque,  and 
speed.  Examples  of  these  classes  are  as  follows: 

(a)  When  a  motor  is  used  on  a  crane  or  an  elevator  it 
must  be  capable  of  developing  a  constant  torque  at  a  variable 
speed,  since  it  is  desired  to  move  a  given  weight  at  different 
speeds. 

(b)  In  some  classes  of  work,  such  as  the  operation  of  a 
motor  used  in  driving  generators   at  a  constant  speed,  the 
motor  will  be  subjected  to  a  varying  load  as  the  output  of 


Fig.  168 


DIRECT-CURRENT  MOTORS 


209 


the  generator  is  changed,  but  its  speed  is  to  remain  constant 
and  hence  it  must  be  capable  of  developing  a  variable  torque 
in  order  that  it  may  carry  the  load. 

(c)  In  certain  classes  of  work  the  motor  will  be  required 
to  develop  a  variable  torque  at  a  variable  speed.  Such  is 
the  case  in  street-car  motors.  The  torque  rsquired  is  a 
maximum  when  the  car  is  being  started  and  the  speed  a 
minimum,  and  as  the  speed  increases  the  torque  decreases. 

Motors  may  then  be  divided  into  three  classes,  according 
to  the  character  of  the  work  to  be  performed,  and  they  must 
develop  either: 

(a)  Constant 
torque     at     variable 
speed. 

(b)  Variable 
torque     at     constant 
speed. 

(c)  Variable 
torque     at     variable 
speed. 

The  shunt  and  the 
compound  motor 
meet  the  require- 
ments in  cases  (a) 
and  (b),  and  the  Figr-  169 

series  motor  operated  from  a  constant-potential  line  generally 
fulfills  the  requirements  for  case  (c).  The  only  motor  that 
naturally  meets  the  requirements  in  case  (a)  is  the  series 
motor  operated  on  a  constant-current  circuit. 

224.  Construction  of  Motors. — The  character  of  the  work 
a  motor  is  to  perform  will  determine  to  a  great  extent  its 
construction.  The  motor  may  be  located  in  an  exposed  place; 
or  it  may  be  in  a  room  filled  with  steam  or  dust  and,  as  a 
result,  it  must  be  practically  enclosed  in  order  to  provide 
ample  protection  to  the  windings,  etc.  If  a  motor  is  to  be 
used  in  a  street  car,  for  example,  its  mechanical  construction 
would  need  to  be  quite  different  from  one  that  was  to  be 
used  on  an  elevator,  as  the  street-car  motor  would,  no  doubt, 
be  subjected  to  more  mechanical  abuse  than  the  elevator 
motor. 


210 


PEACTICAL  APPLIED  ELECTRICITY 


225.     Railway    Motors   and    Their   Control. — There   are   two 
general  methods  for  controlling  railway  motors,  viz, 

(a)  The  rheostatic  method. 

(b)  The     series-parallel     method     (in     combination     with 
rheostat). 

(a)     The  connection  in  the  case  of  the  rheostatic  method 
is  shown  diagrammatically  in  Fig.  172.     Resistance  is  placed 

in  series  with  the  various 
motors  and  by  cutting  this 
resistance  in  and  out  of  cir- 
cuit, the  voltage  impressed 
upon  the  motor  can  be 
changed. 

(b)  The  series-parallel 
method  consists  first  in 
placing  two  motors  in  series 
with  a  resistance  in  circuit 
with  them,  as  shown  in  Fig. 
173,  then  decreasing  the  re- 
sistance until  the  motors 
are  connected  in  series  di- 
rectly across  the  line.  This  constitutes  what  is  called  a 
running  position  as  there  is  no  (I2R)  loss  in  a  starting  resist- 
ance, the  entire  voltage  being  impressed  upon  the  two  motors. 
The  next  connection  places  the  motors  in  parallel  and  a 
resistance  in  series  with 
them,  as  shown  in  Fig.  174. 
This  resistance  is  then  grad- 
ually cut  out  and  the  mo- 
tors are  finally  operating 
directly  across  the  line, 
which  corresponds  to  the 
final  running  position. 

The  control  of  the  switches 
governing  the  connections 
may  be  accomplished  di- 
rectly by  hand  or  by  an 
auxiliary  control.  In  the 
first  case  the  changes  in 


Fig-.  170 


Fig".  171 


connections  are  made  by  a  motorman  on  the  car  platform,  who 
moves  the  handle  of  a  controller.    This  movement  of  the  con- 


DIEECT-CUEEENT  MOTOES 


Supply 


troller  handle  causes  a  cylinder  inside  the  containing  case  to 
rotate.  This  cylinder  has  a  number  of  contact  arms  mounted 
on  its  surface  and  these  make  contact  with  stationary  fingers 
as  the  cylinder  is  rotated.  A  controller  manufactured  by  the 
General  Electric  Company  is  shown  in  Fig.  175.  A  small  handle 

to  the  right  of  the  main   controller 

handle,  as  shown  in  the  figure,  ena- 
bles the  motorman  to  reverse  the  di- 
rection of  rotation  of  the  motors  by 
changing  the  connections.  The  com- 
plete wiring  diagram  of  a  street  car 
is  shown  in  Fig.  176.  Fig.  172 

When   auxiliary   devices   are   used 

to  control  the  connections  of  the  various  motors  the  system  is 
called  a  multiple-unit  control.  When  this  system  is  used,  a 
number  of  cars  can  be  coupled  together  and  the  motors  on  all 


Fig.  173 

of  them  controlled  from  any  car.  The  equipment  of  each  car 
consists  of  a  series-parallel  controller,  whose  electrical  opera- 
tion is  similar  to  that  just  described,  and  so  arranged  that  it  is 
controlled  from  master  controllers  that  are  located  in  the 
motorman's  cabs  at  the  ends  of  the  cars.  The  leads  that 
run  from  the  motor  controllers  to  the  master  controllers  run 


Fig.  174 

the  entire  length  of  the  train,  the  connection  between  cars 
being  made  by  means  of  suitable  couplers.  The  operation 
of  any  one  of  the  master  controllers  will  cause  all  of  the 
motor  controllers  to  operate  in  the  same  way  and  thus  all 


212  PEACTICAL  APPLIED  ELECTRICITY 

of  the  various  motor  connections  throughout  the  train  are 
the  same. 

In  the  Sprague-General  Electric  Multiple-Unit  Control  Sys- 
tem, the  master-controller  circuit  takes  current  direct  from 
the  line  and  the  motor  controllers  are  operated  by  means 
of  solenoids. 

In  the  Westinghouse 
Electric  Company's  Multi- 
ple-Unit Control  System, 
the  motor  controllers  are 
operated  by  compressed 
air,  the  valves  controlling 
the  air  being  governed  by 
the  master  controllers. 
The  master-controller  cir- 
cuit receives  its  current 
from  a  storage  battery. 

226.  Automobile  Motors. 
— The  series  motor  is  uni- 
versally used  for  automo- 
bile work.  The  source  of 
energy  is  a  storage  battery 
and  the  cells  are  so  ar- 
Fig-  175  ranged  that  they  can  be 

connected  in  different  ways,  giving  different  voltages.  This 
variation  in  voltage,  together  with  a  series-parallel  combina- 
tion of  different  sections  in  the  series  field  affords  an  easy 
means  of  controlling  the  speed.  Thus,  if  forty  cells  be  used 
they  may  be  connected  in  four  groups  of  ten  cells  each 
and  these  groups  then  connected  in  parallel;  as  the  speed 
of  the  motor  increases,  the  grouping  of  the  cells  can  be 
changed  and  also  the  series  field  connections.  These  changes 
in  connections  are  governed  by  a  suitable  controller  so  ar- 
ranged that  the  driver  of  the  machine  can  operate  it  by  a 
lever  or  hand  wheel. 

Automobile  motors  are  very  compact  and  usually  con- 
structed with  a  view  to  economy  in  weight.  When  they 
are  located  under  the  car,  they  are  of  the  enclosed  type; 
while  if  they  are  placed  in  an  unexposed  position,  they  can  be 
of  the  semi-enclosed  or  open  type.  In  some  cases  two  mo- 
tors are  provided,  one  being  attached  to  each  wheel  through 


DIEECT-CUEEENT  MOTOES 


213 


4 


Fig.  176 


214: 


PEACTICAL  APPLIED  ELECTRICITY 


a  suitable  transmission,  the  wheels  turning  independent  of 
each  other,  while  in  other  cases  a  single  motor  is  employed, 
the  connection  to  the  wheels  being  made  by  means  of  some 
form  of  differential  gear.  The  various  parts  of  an  automo- 
bile motor  used  by  the  Woods  Electric  Company  are  shown 
in  Fig.  177. 


Fig.  177 

227.  Elevator  and  Crane  Motors. — There  are  many  dif- 
ferent forms  of  elevator  and  crane  motors  on  the  market  and 
the  electrical  operation  of  all  of  them  is  practically  the  same. 
In  the  majority  of  cases  some  kind  of  a  brake  is  provided 
so  that  the  load  may  be  held  after  it  is  raised.  These  brakes 
may  be  either  of  the  friction  or  of  the  dynamic  type. 


Fig.  178 

The  friction  brake  is  usually  controlled  by  a  solenoid.  When 
the  motor  is  operating,  the  solenoid  is  energized  and  the 
brake  does  not  act.  If  the  motor  is  disconnected  from  the 


DIRECT-CURRENT  MOTORS  215 

line  and  the  solenoid  de-energized,  the  brake  clamps  a  pulley 
and  prevents  the  armature  turning. 

In  the  dynamic  brake  the  motor  is  converted  into  a  gen- 
erator and  delivers  current  to  some  local  circuit  while  it  is 
coming  to  rest,  which  results  in  the  motor  stopping  quicker 
than  it  would  otherwise.  The  dynamic  brake  is  usually  used  in 
combination  with  the  friction  brake,  the  friction  brake  be- 
coming operative  after  the  action  of  the  dynamic  brake 
ceases.  A  motor  provided  with  a  friction  brake  is  shown  in 
Fig.  178. 

228.  Efficiency  of  a  Motor. — There  are  three  efficiencies 
'for  a  motor,  namely, 

(a)  Efficiency  of  conversion. 

(b)  Mechanical  efficiency. 

(c)  Commercial   efficiency. 

(a)  The  efficiency  of  conversion  is  the  ratio  of  the  total 
mechanical    power    developed    to    the    total    electrical    power 
supplied  (El),  or 

(P  +  stray-power  losses) 

Efficiency  of  conversion  =  — -  X  100 

El 

(117) 
(P  in  the  above  equation  is  the  power  available  at  the  pulley.) 

(b)  The  mechanical  efficiency  is  the  ratio  of  the  mechan- 
ical power  available  at  the  pulley   (P)   to  the  total  mechan- 
ical power  developed,  or 

P 

Mechanical  efficiency  =  —  —  X  100 

(P  +  stray-power  losses) 

(118). 

(c)  The   commercial   efficiency   is   the   ratio   of  the  avail- 
able output  (P)  to  the  input  (El),  or 

P 

Commercial  efficiency  = X  100  (119) 

El 

The    commercial    efficiency    is    by    far    the    most    important 
of  the  three;  it  includes  all  the  losses  in  the  machine. 

229.     Determining  the  Commercial  Efficiency  by  Test. — The 
commercial  efficiency  of  a  motor  can  be  determined  by  meas- 


216 


PRACTICAL  APPLIED  ELECTRICITY 


uring  the  electrical  input  by  means  of  a  voltmeter  and  an 
ammeter,  and  at  the  same  time  measuring  the  mechanical 
output.  When  the  values  of  these  two  quantities  are  known, 
they  may  be  substituted  in  equation  (119)  and  the  efficiency 
calculated. 

A  satisfactory  way  of  measuring  the  output  of  the  motor 
is  by  means  of  a  Prony  brake.  The  construction  and  opera- 
tion of  this  brake  can  best  be  explained  by  reference  to 
Fig.  179.  The  brake  proper  consists  of  two  parts  (C)  and 
(D)  that  are  held  together  by  two  bolts  (B^  and  (B2).  The 

bolts  are  provided  with  small 
hand  wheels  (Hj)  and  (H2) 
by  means  of  which  the  pres- 
sure of  the  brake  upon  the 
pulley  can  be  varied.  An 
arm  (A)  is  attached  to  the 
brake  and  extends  out  at 
right  angles  to  the  shaft 
upon  which  the  pulley  (P)  is 
Fig.  179  mounted.  When  the  brake  is 

in  use,  the  outer  end  of  the 

arm  (A)  rests  upon  the  platform  of  a  pair  of  scales.  The 
torque  exerted  by  the  armature  in  pound-feet  is  equal  to  the 
net  reading  of  the  scales  in  pounds  multiplied  by  the  hori- 
zontal distance  (L),  in  feet,  between  the  point  where  the  arm 
(A)  rests  upon  the  scales  and  the  center  of  the  shaft.  Call 
the  scale  reading  (W),  then 


T  =  W  X  L 
and  the  output  in  horse-power  will  be  equal  to 

27r  X  T  X  r.p.m. 
h.p.  = 


or 


33  000 


2-rr  X  W  X  L  X  r.p.m. 
h.p.=- 

33000 


(120) 


(121) 


(122) 


The  input,  of  course,  will  be  in  electrical  units  and  either 
the  output  or  input  must  be  changed  before  equation  (119' 
can  be  used  in  calculating  the  efficiency. 


DIEECT-CUEKENT  MOTOES 

[Note.— The  dead  weight  of  the  brake  must  always  be  sub- 
tracted from  the  scale  reading  in  order  to  obtain  the  net 
weight  or  the  value  to  be  used  in  equation  (122)  ]. 

Example.— In  the  test  of  a  motor  by  the  Prony  brake 
method,  the  net  scale  reading  was  thirty  pounds,  the  lever 
arm  of  the  brake  was  two  feet,  and  the  motor  was  running  at 
1000  r.p.m.  What  was  its  commercial  efficiency  if  the  input 
was  91.0  amperes  at  110  volts? 

Solution.— The  output  can  be  obtained  by  substituting  in 
equation  (122),  which  gives 

2:r  X  30  X  2  X  1000 

h.p.  = 

33000 

376  992 

=  11.42 

33000 

The  output  was  then  11.42  horse-power  or  8519.32  watts.    The 
input  was 

91  X  110  =  10  010  watts 
and  the  efficiency  was 

8519.32 

=  85.1 

10  010.00 

Ans.    85.1  per  cent. 


PROBLEMS  ON   DIRECT-CURRENT   MOTORS 

1.  Calculate    the    torque    in    pound-feet,    exerted    by    the 
armature  of  a  motor  wound  with  300  inductors  (simplex  lap 
winding,    singly    re-entrant),    and    revolving    in    a    four-pole 
magnetic  field,  the  flux  (*)  per  pole  being  4  000  000  maxwells 
and  the  armature  current  200  amperes. 

Ans.     281.76  pound-feet. 

2.  If  the  speed  of  the  armature  in  problem    (1)    is  1200 
revolutions   per  minute,  what  is   the  horse-power  output  of 
the  motor?  Ans.    64.3  horse-power. 

3.  Calculate  the  counter  electromotive  force  generated  for 
the  data  given  in  problem  (1)  if  the  speed  is  1200  r.p.m. 

Ans.     240  volts. 


218  PRACTICAL  APPLIED  ELECTEICITY 

4.  Calculate  the  impressed  voltage  for  the  above   motor, 
if  the  armature  resistance  is  .035  ohms,    (Ia)   being  200   am- 
peres and  (Ec)  240  volts.  Ans.     247  volts. 

5.  The   speed  of  a   motor   is   1200   r.p.m.   when  operating 
under    load    and    1250    r.p.m.    when    operating    without    load, 
what  is  its  speed  regulation  in  per  cent? 

Ans.     4.17 —  per  cent. 

6.  Calculate  the  output  of  a  motor  in  horse-power  when  the 
input  is   100  amperes  at  110  volts  and  the   commercial  effi- 
ciency of  the  machine  is  90  per  cent. 

Ans.     13.27  horse-power. 

7.  At  what  speed  must  a  motor  run  in  order  that  its  out- 
put be  50  horse-power,  the  torque  being  263.0  pound-feet? 

Ans.    1000  revolutions  per  minute. 

8.  What  is  the  average  pull  on  each  of  the  inductors  in 
problem   (1)   if  the  inductors  are  located  8  inches  from  the 
center  of  the  armature?  Ans.    1.41 —  pounds. 

9.  The   total   armature    resistance   of   a    six-pole    250-volt 
direct-current  motor,  including  brushes,  brush  contacts,  etc., 
is   .012   ohm.     The   winding   on   the    armature   is   a    simplex 
singly  re-entrant  lap  winding  and  composed  of  600  inductors. 
What  is  the  flux  (<£)  per  pole  when  the  machine  runs  at  900 
r.p.m.  and  takes  a  current  of  300  amperes? 

Ans.     2  738  000  maxwells. 

10.  In  testing  a  motor  by  the  Prony  brake  method,  the 
following  data  were  obtained.     Calculate  the  commercial  effi- 
ciency for  this  particular  load: 

(Net)   Scale  reading  (W)  =  38.88  pounds 

Length  lever  arm          (L)    =3  feet 

Speed  of  armature,  900  revolutions  per  minute 

Impressed  voltage,  220  volts 

Current  input,  75  amperes  Ans.    90+  per  cent. 


CHAPTER  XI 

ARMATURES  FOR  DIRECT-CURRENT  DYNAMOS 

230.  Armature. — An   electrical   conductor,   such   as   a   sim- 
ple loop  of  wire,  moved  in  a  magnetic  field,  so  that  there  is 
an  e.m.f.  induced  in  it,   constitutes   a   simple   armature.     An 
armature  composed  of  a  single  turn  of  wire  is  shown  in  Fig. 
127.    The  e.m.f.  induced  in  such  an  armature  is  unsteady— see 
section    (178) — and   in  order  that  a  practically  steady  e.m.f. 
be  induced  more  turns  of  wire  should  be  used  and  these  vari- 
ous turns  should  be  so  located  and  connected  with  respect  to 
each  other  that  the  e.m.f.  between  the  brushes  remains  almost 
constant. 

The  armature  of  a  commercial  direct-current  dynamo  con- 
sists of  three  principal  parts,  namely, 

(a)  The  armature  core  (sections  231  to  233  inclusive). 

(b)  The  commutator  (sections  234  to  236  inclusive). 

(c)  The  armature  windings  (sections  238  to  251  inclusive). 

231.  Armature  Cores. — The  core  of  an  armature  serves  a 
double  purpose:  it  supports  the  armature  winding  and  it  con- 
ducts the  magnetic  flux  from  the  face  of  one  pole  piece  to 
another. 

Since  the  armature  core  is  moved  relative  to  the  magnetic 
field,  it  becomes  magnetized  in  alternate  directions,  which 
results  in  a  loss  due  to  hysteresis.  There  will  also  be  a  loss, 
as  explained  in  section  (127),  due  to  eddy  currents.  The 
hysteresis  loss  can  be  reduced  to  a  minimum  by  using  a 
grade  of  iron  whose  hysteretic  constant  is  low,  while  the 
eddy-current  loss  is  reduced  by  building  the  armature  cores 
of  thin  soft  iron  or  sheet  steel  disks  insulated  from  each 
other  by  rust,  insulating  varnish,  or  paper.  The  disks  are 
always  placed  in  such  a  position  with  respect  to  the  magnetic 
field  that  their  plane  is  parallel  to  the  magnetic  flux. 

Armature  cores  are  of  two  general  types,  smooth  cores  and 
slotted,  or  tunneled,  cores.  In  the  smooth  core  type,  the  arma- 

219 


220 


PEACT1CAL  APPLIED  ELECTKICITY 


ture  windings  are  placed  upon  the  surface  of  the  cores, 
while  in  the  slotted,  or  tunneled,  type,  they  are  placed  in  slots 
or  openings  cut  in  the  outer  edge  of  the  core  stampings. 
The  mechanical  and  electrical  construction  of  the  slotted, 
or  tunneled,  type  is  better  than  that  of  the  smooth  core 


Fig.  180 


Fig.  181 


type,  because  the  length  of  the  air  gap  in  the  magnetic  circuit 
is  reduced,  and  the  conductors  are  held  rigidly  in  place, 
which  prevents  their  moving  back  and  forth  and  the  likeli- 
hood of  injury  to  the  insulation  on  them  is  thus  greatly 
reduced. 

232.     Armature-Core  Stampings. — The  stampings  used  in  the 
construction  of  armature  cores   assume  a   number  of  differ- 


Fig.  183 


ent  forms,  depending  upon  the  size  and  kind  of  armature 
for  which  they  are  intended.  In  the  construction  of  small 
armature  cores  the  disks  are  punched  in  one  piece,  as  shown 
in  Figs.  180  and  181.  The  disks  used  in  the  construction 
of  large  cores  are  made  in  sections,  as  shown  in  Figs.  182 
and  183,  and  these  various  sections  are  then  mounted  upon 


ARMATURES 


221 


an  auxiliary  support  called  a  spider,  which  may  assume  a 
number  of  different  forms.    A  spider  upon  which  the  disks 


J 


Fig.  185 


shown  in  Fig.  182  can  be  mounted  is  shown  in  Fig.  184. 
Such  a  core  would  usually  be  used  for  a  ring  winding.  A 
spider  upon  which  the  disks  shown 
in  Fig.  183  can  be  mounted  is 
shown  in  Fig.  185.  The  dovetail 
notches  or  extensions  on  the  stamp- 
ings fit  into  dovetail  extensions  or 
notches  on  the  spider  arms.  The 
various  lamina?  are  held  together 
by  means  of  bolts  (B)  and  end 
plates  (Pi)  and  (P2),  as  shown  in 
Fig.  188. 

233.  Ventilation.— On  account  of 
the  heat  generated  in  the  armature 
cores,  due  to  hysteresis  and  eddy 
currents  in  the  iron,  and  the  (I2R) 
losses  in  the  armature  conductors, 
some  means  of  ventilation  must  be 
provided  in  order  to  prevent  an  ex- 
cessive temperature  rise.  The 
means  usually  employed  in  venti- 
lating the  armajture  cores,  especially  in  the  larger  machines 
is  to  separate  the  cone  disks  at  certain  intervals  along 
the  axis  of  the  core.  These  openings  between  the  disks 


Fig.  186 


222 


PEACTICAL  APPLIED  ELECTEICITY 


called  ventilating  ducts,  can  be  made  by  placing  a  piece  of 
metal  on  edge,  as  shown  in  Figs.  187  and  188,  and  fastening 
them  to  the  disk.  These  ventilating  ducts  are  usually  spaced 
from  2  to  4  inches  apart. 


Fig.  187 


Fig.  188 


234.  The  Commutator. — The  commutator  usually  consists 
of  a  number  of  similar  wedge-shaped  pieces  of  copper  clamped 
between  two  rings,  as  shown  in  Figs.  189  and  190,  and  in- 
sulated from  each  other  by  mica  or  other  insulating  material 
whose  wearing  qualities  are  practically  the  same  as  that  of 
copper.  Amber  mica  is  usually  used  for  this  purpose. 


Fig.  189 


Fig.  190 


The  commutator  shown  in  Fig.  189  is  for  a  small  machine, 
while  the  one  shown  in  Fig.  190  is  for  a  large  machine. 

235.  Commutator  Risers. — The  various  commutator  seg- 
ments are  connected  to  the  armature  winding  by  means  of 
commutator  risers.  These  risers  consist  of  pieces  of  metal 
that  project  radially  from  the  end  of  the  commutator  toward 
the  surface  of  the  armature.  In  the  case  of  small  machines 
they  are  formed  as  a  part  of  the  commutator  segment.  In 
large  machines  a  piece  of  metal  is  soldered  or  brazed  into  a 


AEMATURES  223 

groove  cut  in  the  end  of  the  commutator  bar  before  the  com- 
mutator is  assembled. 

236.  Construction  of  the  Commutator. — In  constructing  the 
commutator  the   segments   and   insulation   are   placed   inside 
a  heavy  clamping  ring  and  the  inside  of  the  commutator  is 
turned  down  to  the  proper  dimension.     It  is  then   clamped 
between  its  own  rings    (Rj)    and    (R2),  Fig.   189,  before  the 
first  clamping  ring  is  removed.     When  it  is  rigidly  fastened 
in    place,    the    outer    ring    may    be    removed    and    the    outer 
surface  turned  down  to  the  proper  dimensions  and  form. 

237.  Brushes   and    Brush    Holders. — The   brushes    used    on 
dynamos  are  usually  made  from  hard  blocks  of  what  is  known 
as  graphitic  carbon.     In  some  special  cases,  however,  metal 
brushes    are    used,    especially    when    a    very    low    resistance 
brush  is  desired,  or  they  may  be  a  combination  of  metal  and 
carbon.     The  carbon  brushes  have  the  advantage  of  wearing 
well  mechanically   and   they   are   self-lubricating,   giving   the 
commutator  a  very  smooth  surface.    They  also  have  a  higher 
resistance  than  the  metal,   or  combination   brushes   and,   as 
*a  result,  reduce  the  tendency  for  sparking  to  occur  at  the 
commutator   when   the   brush   bridges   two   commutator    seg- 
ments connected  to  an  element  of  the  armature  winding  that 
may  be  undergoing  commutation.     The  tendency  for   spark- 
ing at  the  commutator,  due  to  the  cause  just  mentioned,  is 
not  very  great  in  low  voltage  machines,  such  as  those  used 
in  electroplating   and,   as   a  result,  copper  or   copper  gauze 
brushes  are  used,  thus  reducing  the  total  resistance  of  the 
circuit. 

Brushes  are  usually  mounted  so  that  they  make  an  angle 
with  the  surface  of  the  commutator,  although  in  some  cases 
they  are  set  radial,  especially  in  cases  where  the  direction 
of  rotation  of  the  machine  is  to  change,  as  in  street-car 
motors. 

The  brushes  are  supported  in  individual  holders,  and  these 
holders  are  mounted  on  arms  called  brush-holder  arms,  which 
in  turn  are  mounted  on  rings  that  are  concentric  with  the 
commutator  and  called  rockers.  The  brush  holders  should 
be  so  constructed  that  the  pressure  of  the  brush  on  the 
commutator  can  be  adjusted  and  the  electricity  be  conducted 
to  the  brush  holders  through  a  path  other  than  that  formed  by 
the  spring  used  in  holding  the  brush  upon  the  commutator. 


224 


PKACTICAL  APPLIED  ELECTKICITY 


Fig.  191 


The  rockers  supporting  the  brush-holder  arms  are  mounted 

on  the  front  bearing  in  small  machines,  and  on  projecting 

arms  from  the  magnetic  frame 
in  large  machines.  The  rockers 
are  always  so  arranged  that  they 
can  be  moved  by  a  lever  or  a 
specially  arranged  hand  wheel, 
which  affords  a  means  of  ad- 
justing them  to  their  proper  po- 
sition on  the  commutator.  A 
brush  and  brush  holder  are 
shown  in  Fig.  191.  The  brushes 
are  connected  to  the  stationary 
part  of  the  holder  by  means  of 

flexible  copper  conductors. 

238.     Armature     Windings. — Armature     windings     may     be 

classified  according  to  the  manner  in  which  they  are  placed 

upon  the  core,  as  follows: 

(a)  Ring   windings. 

(b)  Drum  windings. 

(c)  Disk  windings. 

(a)  In     ring     windings 
the  conductors  are  placed 
upon    a    ring-shaped    core, 
the  winding  passing 
through  the  interior  of  the 
ring,  as  shown  in  Fig.  192. 
These  windings  are  some- 
times  referred   to  as    hel- 
ical windings. 

(b)  In    drum    windings 
the  winding  is  placed  en- 
tirely upon  the  surface  of 
the    drum,    when    smooth 

cores  are  used,  or  in  slots  or  tunnels  cut  in  the  surface  of  the 
core.     Such  an  armature  winding  is  shown  in  Fig.  193. 

(c)  In  the  disk  windings  the  cores  upon  which  the  wind- 
ing is  placed  are  shorter  and  larger  in  diameter  in  propor- 
tion than  they  are  in  the  case  of  drum  windings.     The  in- 
ductors  correspond  to  the   spokes  of  a  wheel  and  are   con- 


Fig.  192 


ARMATURES 


225 


nected  in  a  manner  similar  to  those  in  the  drum  winding.     A 
disk-wound  armature  is  shown  in  Fig.  194. 

In  addition  to  the  above  classification  of  armature  wind- 


Fig.  193 

ings,  they  may  be  grouped  into  two  types,  depending  upon 
whether  the  winding  constitutes  an  open  or  closed  circuit,  viz, 


Fig.  194 

(a)  Closed-coil  windings. 

(b)  Open-coil  windings. 

(a)     The   closed-coil   windings   have   all   the   inductors   in- 


226  PEACTICAL  APPLIED  ELECTRICITY 

terconnected,  so  that  the  e.m.f.'s  induced  in  them  are  always 
effective  in  producing  a  current  in  the  external  circuit,  ex 
cept  when  a  certain  part  of  the  winding  is  undergoing  com- 
mutation. This  type  of  winding  gives  a  very  steady  current 
and  the  difficulties  due  to  sparking  are  considerably  less 
than  in  the  open-coil  type. 

(b)  The  open-coil  windings  have  the  inductors  and  com- 
mutator segments  so  arranged  that  the  e.m.f.'s  induced  in 
the  windings  are  only  effective  in  producing  a  current  in 
the  external  circuit  when  the  coil  is  undergoing  commuta- 
tion. This  type  of  winding  does  not  give  as  steady  a  cur- 
rent as  the  closed-coil  type  and  considerable  trouble  is  en- 
countered in  commutation  due  to  sparking.  The  open-coil 
winding  is  used  mostly  (in  the  case  of  direct-current  ma- 
chines) for  constant-current  arc-lighting  machines. 

239.  Armature  Inductors. — That  part  of  the  armature  wind- 
ing in  which  an  e.m.f.  is  induced  is  called  an  armature  in- 
ductor. The  terms  conductor  and  inductor  have  been  used 
in  the  same  sense  up  to  the  present  time,  but  in  speaking 
of  armature  windings  from  now  on  the  term  armature  in- 
ductor will  be  used.  Thus,  in  the  case  of  a  ring  winding, 
as  shown  in  Fig.  192,  there  will  be  one  inductor  per  turn,  it 
being  the  outer  portion  of  the  turn,  as  that  is  the  only  part 
of  the  turn  in  which  there  is  an  e.m.f.  induced.  In  the  drum 
winding,  as  shown  in  Fig.  193,  there  will  be  two  inductors 
per  turn,  because  both  sides  of  the  turn  have  e.m.f.'s  in- 
duced in  them. 

The  e.m.f.'s  induced  in  the  conductors  in  the  case  of  the 
ring  winding  are  all  acting  in  series  and  in  the  same  direc- 
tion, the  inductors  being  connected  by  the  part  of  each  turn 
that  passes  through  the  ring.  If  this  return  portion  of  each 
turn  were  placed  on  the  outside  of  the  cores,  as  in  the  case 
of  a  drum  winding,  it  would  become  an  inductor  and  there 
would  be  an  e.m.f.  induced  in  it,  but  the  direction  of  the 
induced  e.m.f.  would  be  such,  if  the  two  parts  of  the  coil 
were  under  poles  of  the  sam^  polarity,  that  it  would  tend  to 
neutralize  the  e.m.f.  in  the  other  portion  of  the  coil  or  in- 
ductor. In  order  that  the  e.m.f.  in  the  two  parts  of  an  arma- 
ture coil,  in  the  case  of  a  drum  winding,  may  act  in  series 
and  in  the  same  direction,  they  are  so  placed  on  the  core 
that  the  two  parts  are  under  poles  of  opposite  polarity. 


ARMATURES  227 

240.  Element   of  Armature   Winding.— The  element  of  an 
armature  winding  is  that  part  of  the  winding  which  termi- 
nates at  two  consecutive  commutator  segments,  as  the  wind- 
ing is  being  traced  out.     In  a  ring  winding  there  may  be  a 
commutator  segment  connected  between  all  the  turns,  then 
an  element  would  consist  of  a  single  turn  and  one  inductor. 
The  number  of  inductors  and  turns  per  element  in  the  case 
of  a  ring  winding  is  the  same,  and  the  number  of  conductors 
or  turns  per  element  will  depend  upon  the  relation   of  the 
number   of   commutator    segments    (K)    and    the    number   of 
inductors  (Z).     In  the  drum  winding  a  commutator  segment 
may   be    connected    between    all    the    turns    and   an    element 
would    consist    of   a    single    turn,    or   two    inductors.      There 
will  always  be  twice  as  many  inductors  per  element  as  there 
are  turns  in  the  case  of  drum  windings. 

241.  Armature  Coil. — In  winding  armatures  a   number  of 
turns   are  usually   placed   together   and   insulated   as    a   unit 
and  this  unit,  called  a  coil,  is  placed  upon  the  armature  core. 
The  method  of  forming  and  insulating  the  coils  depends  en- 
tirely upon  the  kind  of  armature  they  are  intended  for,  their 
insulation  being  better  and  greater  care  is  usually  taken  in 
their  construction  when  they  are  to  be  used  on  a  high  volt- 
age machine.     In  some  cases  the  winding  is  placed  directly 
on  the  armature  core. 

A  coil  may  correspond  to  an  element  of  the  winding  or 
the  number  of  inductors  per  coil  may  be  greater  or  less 
than  the  number  of  inductors  per  element.  Thus,  two  or 
more  coils  may  be  connected  in  series  to  form  an  element, 
or  taps  may  be  taken  off  the  coil,  only  part  of  the  coil  being 
used  for  an  element. 

242.  Number  of  Commutator  Segments. — In  the  case  of  a 
simple   ring  winding,   the   maximum   number  of  commutator 
bars  (K)  that  it  is  possible  to  have  is  the  same  as  the  num- 
ber of  turns  or  inductors  on  the  armature  cores.     The  num- 
ber of  bars  may,  of  course,  be  less  than  the  number  of  in- 
ductors, as  each  element  may  be  composed  of  a  number  of 
inductors.      In    general,    if    (M)    represents    the    number    of 
turns    in    each    element    of   the   winding    and    (Z)    the    total 
number   of  inductors,   the   number   of   commutator   segments 
will  be  equal  to 


22S  PRACTICAL  APPLIED  ELECTRICITY 

K  =  —  (123) 

M 

The  number  (M)  can  have  any  value  so  long  as  (Z)  divided' 
by  (M)  gives  a  whole  number  as  a  quotient. 

The  maximum  number  of  commutator  bars  that  it  is  pos^ 
sible  to  have  in  a  commutator  to  be  used  with  a  simple  drunj 
winding  is  equal  to 

Z 

K  =  -  (124) 

2M 

In  the  above  equation,  (M)  represents  the  number  of  turns 
in  series  in  each  element  of  the  winding  and  since  there  are' 
two  inductors  per  turn  for  a  drum  winding,  (2M)  is  the 
total  number  of  inductors  per  element.  The  number  (M) 
can  have  any  value,  even  or  odd,  but  (2M)  will  always  be? 
even  and,  since  (K  -r-  2M)  must  give  a  whole  number,  as  in 
the  previous  case,  (Z)  must  be  even. 

243.  Pitch  of  Winding  and  Field  Step.— It  was  explained 
in  section  (239)  that  the  two  inductors  composing  a  single 
turn  in  the  case  of  a  simple  drum  winding  had  to  be  placed 
in  such  a  position  on  the  armature  that  the  inductors  were 
under  poles  of  opposite  polarity.  In  the  case  of  a  ring  wind- 
ing, as  explained  in  section  (239),  the  inductors  can  be  placed 
under  a  pole  of  the  same  polarity  because  they  are  con- 
nected by  a  conductor  that  passes  through  the  center  of  the 
ring  and  in  which  there  is  practically  no  induced  e.m.f.  The 
field  step  in  the  case  of  a  winding  is  unity  when  the  distance 
between  one  inductor  and  the  ne&t  in  order,  in  tracing 
through  the  winding,  corresponds  very  nearly  to  the  distance 
between  the  centers  of  adjacent  unlike  poles.  The  field  step 
then  for  a  simple  ring  winding  is  zero  and  for  a  simple  drum 
winding  is  unity.  It  may  be  greater  than  these  values  for  the 
two  windings,  but  the  connections  required  to  join  the  ends 
of  the  inductors  would  be  unnecessarily  increased  in  length, 
which  would  mean  an  increase  in  the  cost  of  copper  required 
for  the  winding  and  an  increase  in  the  resistance  of  the 
armature. 

The  pitch  of  a  winding  is  the  distance  from  one  inductor 
of  the  winding  to  the  next  inductor  in  order.  This  distance 
is  usually  measured  in  terms  of  the  number  of  inductors 
passed  over,  or  it  may  be  measured  in  terms  of  the  number 


AEMATUKES  229 

of  half  coils,  slots,  or  distance  on  the  surface  of  the  arma- 
ture. An  example  would  perhaps  show  more  clearly  the 
exact  meaning  of  the  term  "pitch."  Let  the  inductors  on  a 
certain  drum-wound  armature  be  numbered  consecutively 
around  the  armature  starting  with  number  (1).  If  inductor 
number  (1)  is  joined  at  the  back  end  of  the  armature  (end 
opposite  the  commutator)  to  inductor  (14),  and  inductor  (14) 
Is  joined  at  the  front  end  of  the  armature  to  inductor  (27), 
etc.,  the  pitch  of  the  winding  would  be  the  same  at  both  ends 
and  equal  to  13.  The  front  pitch  is  represented  by  the 
symbol  (Yf)  and  the  back  pitch  by  symbol  (Yb).  These 
pitches  are  both  positive  in  sign  when  they  are  measured 
in  the  same  direction  around  the  armature.  If,  in  the  above 
case,  inductor  (1)  be  joined  to  inductor  (16)  at  the  back 
end,  and  inductor  (16)  be  joined  to  inductor  (3)  at  the  front 
end,  and  inductor  (3)  be  joined  to  inductor  (18)  at  the  back 
end,  etc.,  the  front  pitch  would  be  negative  and  the  back  pitch 
positive.  Their  values  would  be  (Yb)  =  15  and  (Yf)  =  — 13. 

The  average  pitch  (Yav)  in  any  case  is  equal  to  the  aver- 
age of  the  front  and  the  back  pitches  regardless  of  their  signs. 
For  the  first  winding  (Yav)  would  be  [(13-f  13) -=- 2]  =  13, 
and  for  the  second  winding  (Yav)  would  be  [(15  -f-  13)  -r-  2] 
=  14.  The  resultant  pitch  (Yr)  of  any  winding  is  the  alge- 
braic sum  of  the  two  pitches.  For  the  first  winding  (Yr) 
would  be  (15)  +  (—13)  ==  2. 

The  commutator  pitch  is  the  interval  between  the  com- 
mutator segments  connected  to  an  element  of  the  winding 
expressed  in  terms  of  the  number  of  commutator  segments. 

244.  Types  of  Ring  Windings. — There  are  two  types  of 
ring  windings: 

(a)  Spirally-wound  ring  windings. 

(b)  Series-connected  wave-wound  ring  windings. 

(a)  In  the  spirally-wound  ring  armature,  the  winding  forms 
a  closed  helix,  as  shown  in  Fig.  192.  There  will  be  (p)  points 

on  the  commutator (p)  represents  the  number  of  magnet 

poles where  brushes  may  be  connected  to  conduct  the  elec- 
tricity to  and  from  the  armature  winding.  The  proper  loca- 
tion of  the  brushes  is  shown  in  the  figure  and  the  number 
of  paths  (b)  through  such  a  winding  is  equal  to  the  number 
of  poles  (p).  The  current  capacity  of  this  winding  will  be 
greater  than  that  of  a  bipolar  machine  if  the  same  size  wire 
is  used  in  the  winding:  and  the  e.m.f.'s  will  be  the  same  if 


230 


PRACTICAL  APPLIED  ELECTKICITY 


the  field  strength,  speed,  and  number  of  inductors  in  series 
are  the  same  in  both  cases.  The  e.m.f.  equation  for  such  a 
machine  is 

Z  X  *  X  P  X  r.p.m. 

E=  (125) 

108  x  60  X  b 

The  number  of  brushes  can 
be  made  less  than  the  num- 
ber of  poles  by  permanently 
connecting  the  various  com- 
mutator segments  together 
that  are  always  at  the  same 
potential. 

(b)  In  the  series -con- 
nected ring  winding,  the  va- 
rious turns  are  connected  in 
series.  In  this  arrangement 
there  will  always  be  two 
paths  in  parallel  through  the 
armature,  regardless  of  the 
number  of  poles.  Armatures 

wound  with  this  kind  of  a  winding  are  called  two-circuit,  or 
series-wound,  armatures.  Only  one  set  of  brushes  iB  required, 
but  a  maximum  of  $p  -f-  2)  sets  can  be  used. 

In  calculating  the  e.m.f.  that  will  be  developed  in  a  wind- 
ing of  this  kind,  equation  (125)  can  be  used  and  (b)  will 
always  be  equal  to  2.  The  armatures  of  the  machines  are 
usually  series  wound  when  their  output  is  to  be  at  a  high 
voltage  and  low  current,  while  if  the  output  is  to  be  at  a  low 
voltage  and  large  current,  they  are  parallel  wound. 

245.  Types  of  Drum  Windings. — Drum  windings  (closed- 
coil)  are  of  two  kinds: 

(a)  Lap  windings. 

(b)  Wave  windings. 

(a)  A  simple  (simplex)  lap  winding  is  shown  in  Fig.  195 
and  a  developed  form  of  the  same  winding  is  shown  in  Fig. 
196.  It  will  be  observed  that  the  front  and  the  back  pitches 
differ  in  sign,  or  the  winding  laps  back  upon  itself.  The  num- 
ber of  paths  (b)  in  parallel  through  an  armature  wound  with 
a  simple  (simplex)  lap  winding  is  equal  to  the  number  of 
poles  (p).  The  number  of  sets  of  brushes  required  in  order 
that  all  the  inductors  be  effective  in  producing  a  current  in 


Fig.  195 


ARMATURES 


231 


the  external  circuit  is  equal  to  (p).  Lap  windings  are  usu- 
ally used  on  armatures  whose  output  is  at  a  low  voltage 
and  large  current. 

(b)  A  simple  (simplex)  wave  winding  is  shown  in  Figs. 
197  and  198.  It  will  be  observed  that  both  the  front  and  the 
back  pitches  are  of  the  same  sign  and  the  winding  advances 
around  the  armature  in  the  form  of  waves.  There  will  be 
only  two  paths  through  an  armature  wound  with  a  simple 
(simplex)  wave  winding  regardless  of  the  number  of  poles. 
Only  two  sets  of  brushes  are  required  for  such  a  winding, 


ic  id,  j  e  |  f  |  9  |  M  t  |  j  |  k|  i  |m|a|  b  |c  \d 
Fig-.  196 


but  as  many  as  (p)  sets  can  be  used.  Wave  windings  are 
usually  used  on  armatures  whose  output  is  at  a  high  volt' 
age  and  low  current. 

If  the  front  and  the  back  pitches  in  a  wave  winding  be  so 
chosen  that  in  starting  with  a  commutator  segment  and  pass- 
ing through  an  element  of  the  winding  in  a  clockwise  direc- 
tion you  arrive  at  a  segment  to  the  right  of  the  one  from 
which  you  started,  the  winding  is  said  to  be  progressive;  if 
the  segment  is  to  the  left  of  the  one  from  which  you  started 
the  winding  is  said  to  be  retrogressive. 

If  the  front  and  back  pitches  in  a  wave  winding  be  so 
chosen  that  in  starting  with  a  given  commutator  segment 
and,  after  passing  in  a  clockwise  direction  through  as  many 
elements  of  the  winding  as  there  are  pairs  of  poles,  you 
arrive  at  a  segment  to  the  right  of  the  one  from  which  you 
started,  the  winding  is  said  to  be  progressive;  and  if  the  seg- 
ments be  to  the  left  of  the  one  from  which  you  started, 
the  winding  is  said  to  be  retrogressive. 

When  the  average  pitch  of  a  winding  differs  considerably 


232 


PEACTICAL  APPLIED  ELECTKICITY 


from  the  number  of  inductors  (Z)  divided  by  the  poles  (p), 
the  winding  is  called  a  chord  winding. 

246.  Multiplex  Windings.— 
Armatures  may  be  wound 
with  two  or  more  independent 
windings,  the  inductors  and 
the  commutator  segments  of 
the  two  windings  being  sand- 
wiched between  each  other, 
as  shown  in  Fig.  199.  A 
winding  composed  of  two  in- 
dependent windings  is  called 
a  duplex  winding;  one  com- 
posed of  three  independent 
Yav=6  windings  is  called  a  triplex 
197  5  winding,  etc.  The  brushes 

must,  of  course,  be  increased 

in  width,  if  the  commutator  segments  remain  the  same  in 
breadth  when  a  multiplex  winding  is  used,  in  order  that  the 
current  may  be  collected  from  all  the  various  windings  at 
the  same  time. 

247.  Re-Entrancy. — In  section  (238)  it  was  stated  that  a 
winding  which  closes  upon  itself  is  called  a  closed-circuit  wind- 
ing. Such  a  winding  is  also  known  as  a  re-entrant  winding, 
because  it  re-enters  upon  itself.  A  winding  is  said  to  be  singly 


m|n|o|p|a|b|c|dJe|fJg|K|t[j|k|l|m|n| 
Fig.  198 

re-entrant  when  the  entire  winding  must  be  traced  through 
before  you  return  to  the  inductor  from  which  you  started. 
If  only  one-half  of  the  winding  need  be  traced  out  before  the 
inductor  from  which  you  started  is  again  reached,  the  wind- 
ing is  said  to  be  doubly  re-entrant.  Likewise  only  one-third 
of  the  winding  is  passed  through  in  a  triply  re-entrant  wind- 


ARMATURES 


233 


Fig.  199 


ing  before  you  return  to  the  conductor  from  which  you  started, 

and  so  on  for  multiply  re-entrant  windings. 
The    term    re-entrancy    as 

used  in  the  remainder  of  the 

chapter    has    a   meaning    en- 

tirely different  than  that  just 

given,    it    being    used    as    a 

factor     in     determining     the 

number    of    circuits    between 

positive  and  negative  brushes. 

In  the  above  definition  of  re- 

entrancy,  there  would  be  no 

difference  between  the  multi- 

plicity and  the  re-entrancy  of 

a    winding.      A     simplex    or 

multiplex    winding,    however, 

may  be  singly  or  multiply  re- 

entrant,  and   the  re-entrancy 

in  the  case  of  a  lap  winding  is  equal  to  the  total  number  of 

paths  through  the  armature  divided  by  the  product  of  the 

number  of  poles  and  the  multiplicity  of  the  winding,  and  in 

the  case  of  the  wave  winding 
it  is  equal  tc  the  total  num- 
ber of  paths  divided  by  twice 
the  multiplicity  of  the  wind- 
ing. The  winding  shown  in 
Fig.  200  is  simplex  doubly  re-t 
entrant,  and  the  one  shown  in 
Fig.  199  is  duplex  singly  re- 
entrant. The  number  of  paths 
through  the  winding  is  the 
same  in  both  cases. 

248.  Number  of  Paths 
Through  Armature  Windings. 
—  As  stated  in  section  (244), 
the  number  of  paths  in  par- 

allel (b)  for  a  simplex  spirally-wound  ring  is   (p),  and  for  a 

simplex  series-wound  ring  (2).    When  such  windings  are  made 

multiplex,  the  number  of  paths  is  increased,  the  number  in 

the  second  case  being  equal  to  the  original  number  multiplied 

by  the  multiplicity  of  the  winding.     Thus  a  triplex   series- 


Fig.  200 


234  PRACTICAL  APPLIED  ELECTRICITY 

wound  ring  winding  would  have  (3X2)  paths  in  parallel,  and 
a  duplex  spirally-wound  ring  winding  would  have  (2Xp)  paths 
in  parallel.  Winding  tables  are  given  in  Chapter  20,  which 
show  the  relation  between  the  multiplicity,  the  re-entrancy, 
the  number  of  paths,  the  number  of  inductors  in  series  in 
each  path,  etc. 

A  closed-coil  drum  winding  must  satisfy  the  following  con- 
ditions. No  drum  winding  can  have  an  odd  number  of  in- 
ductors, for  that  would  be  equivalent  to  not  having  a  whole 
number  of  turns.  The  even-numbered  inductors  may  be  re- 
garded as  the  returns  for  the  odd-numbered  inductors,  or 
vice  versa,  and  both  the  front  and  back  pitches  must  always 
be  odd  in  simplex  windings  in  order  that  you  pass  from  an 
odd  to  an  even  numbered  inductor  at  one  end  of  the  arma- 
ture and  from  an  even  to  an  odd  numbered  inductor  at  the 
other  end  in  tracing  out  the  winding. 

The  front  and  back  pitches  should  be  approximately  equal 
and  correspond  in  value  to  (Z  <•*-  p)  in  order  that  the  in- 
ductors connected  in  series  and  moving  under  poles  of  oppo- 
site polarity  have  their  e.m.f.'s  additive. 

249.  Choice  of  Front  and  Back  Pitch  for  a  Given  Number 
of  Inductors. —  (A)  Lap  and  wave  windings  in  general. 

(a)  All  the  elements  or  coils  composing  the  winding  must 
be  similar,  both  mechanically  and  electrically,  and  must  be 
arranged  symmetrically  with  respect  to  each  other  and  the 
armature  core. 

(b)  In  a  simplex  winding  each  inductor  must  be  encoun- 
tered only  once  and  the  winding  must  be  re-entrant. 

(c)  If  the  winding  is  multiplex,  each  of  the  simplex  wind- 
ings composing  it  must  fulfill  condition  (b). 

(B)    Choice  of  front  and  back  pitch  for  lap  windings. 

(a)  Front  and  back  pitches  must  be  opposite  in  sign. 

(b)  •  The  front  and  back  pitches  must  be  numerically  un- 
equal, for  if  they  were  equal  the  coil  would  be  short-circuited 
upon  itself. 

(c)  The  front  and  back  pitches  must  differ  by  2  in  the 
case  of  a  simplex  lap  winding;  that  is, 

Yb  -f  Yf  ==   ±  2 

(d)  The  front  and  back  pitches  differ  by  2  X  in  the  case 


AEMATUKES 

of  a  multiplex  winding,  (X)  being  the  number  of  independent 
simplex  windings  composing  the  multiplex  winding. 

(e)  The  number  of  inductors  (Z)  must  be  an  even  num- 
ber. If  the  winding  .is  placed  on  a  slotted  armature  the 
number  of  inductors  must  be  a  multiple  of  the  number  or 
slots.  The  number  of  slots  may  be  even  or  odd. 

(C)     Choice  of  front  and  back  pitches  for  wave  windings. 

(a)  The  front  and  back  pitches  must  be  alike  in  sign,  and 
odd. 

(b)  The   front  and   back   pitches   may   be   equal,   or  they 
may  differ  by  two  or  any  multiple  of  two.     It  is  customary 
to  make  them  nearly  equal  to  (Z-f-p). 

(c)  The  number  of  inductors    (Z)   for  a  simplex  winding 
should  comply  with  the  equation 

Z  =  P  Yav  ±  2 

(d)  And  for  a  multiple  winding: 

Z  =  P  Yav  ±  2  X 

250.  Armature  Winding  Table.— Tables  I,  J,  and  K  in  Chap- 
ter 20  give  the  values  of  the  various  quantities  for  the  differ- 
ent types  of  armature  windings.     The  symbols  used  in  these 
tables  represent  the  following  quantities: 

.   z  =  the  total  number  of  inductors  on  the  armature 

X  =  the  number  of  independent  windings 

b  =  the  total  number  of  paths  through  the  armature 

b'i  =  the  number  of  paths  in  parallel  in  each  winding 

m  =  the  field  steps 

y  =  the  resultant  pitch 

Yk=  the  commutator  pitch 

Yf  ==  the  front  pitch 

Yh  =  the  back  pitch 

K  =  the  number  of  commutator  segments 

g  =  the  number  of  inductors  per  group 

G  =  the  total  number  of  groups 
Yav    =  the  average  pitch 

Note. — The  tables  given  in  Chapter  20  were  made  up  by  the 
use  of  equations  given  in  "Design  of  Dynamos"  by  S.  P. 
Thompson. 

251.  Equipotential  Connections. — The  e.m.f.'s  generated  in 
the  various  paths  that  are  connected  in  parallel  in  any  arma- 
ture winding  will,  as  a  rule,  differ  in  value  due  to  inequali- 


236  PRACTICAL  APPLIED  ELECTRICITY 

ties  in  winding,  location  in  magnetic  field,  armature  out 
of  center,  etc.  This  difference  in  e.m.f.  in  the  various  paths 
will  result  in  unequal  currents  in  the  different  paths  through 
the  armature.  In  order  to  reduce  this  unbalanced  condi- 
tion as  much  as  possible  the  points  in  the  winding  that  are 
supposed  to  be  at  the  same  potential  are  connected  by  heavy 
copper  leads,  called  equipotential  connections. 


CHAPTER  XII 

STORAGE    BATTERIES,    THEIR    APPLICATIONS    AND 
MANAGEMENT 

252.  The  Storage  Cell. — A  storage  cell,  secondary  cell,  01 
accumulator,   as  it  is  variously   called,   is   a  voltaic   cell  in 
which  a  chemical  action  is  first  produced  by  an  electrical  cur- 
rent through  the  cell  from  some  external  source  of  energy; 
after  which  the  cell  is  capable  of  delivering  a  current  to  an 
external  circuit  by  means  of  a  secondary  or  reversed  chem- 
ical action.     The  process  of  storing  the  electrical  energy  by 
sending  a  current  through  the  cell  from  some  external  source 
of  energy  is  called  charging.    When  the  cell  is  producing  a 
current  in  an  external  circuit  or  it  is  supplying  energy  it  is 
said  to  be  discharging. 

In  charging  a  storage  cell  a  larger  voltage  is  required  be- 
tween the  terminals  of  the  cell  than  the  cell  is  capable  of  pro- 
ducing on  discharge,  on  account  of  the  internal  resistance  of 
the  cell  and  an  action  on  the  surface  of  the  plates  similar  to 
polarization  in  the  primary  cell.  The  (IR)  drop  in  the  cell 
opposes  the  free  flow  of  the  electricity  through  the  cell,  both 
on  discharge  and  charge,  and  the  energy  the  cell  is  capable 
of  supplying  on  discharge  is  less  than  the  energy  input  to 
the  cell  when  it  is  being  charged.  No  storage  cell,  as  a  re- 
sult, can  have  an  efficiency  of  100  per  cent,  the  efficiency 
decreasing  with  an  increase  in  internal  resistance.  The 
greater  the  internal  resistance  the  greater  the  variation  in 
the  value  of  the  terminal  voltage  with  a  change  in  load. 

253.  Types  of  Storage  Cells. — Storage  cells  may  be  divided 
into  two   main   groups,   according  to   the   kind   of  materials 
used  in  the  construction  of  the  plates,  viz,  lead  storage  cells 
(sections   254   to   274   inclusive),   and    non-lead    storage   cells 
(sections  275  to  278  inclusive). 

254.  Lead  Storage  Cells. — In  the  construction  of  the  lead 
storage  battery,  the  cathode  is  made  of  lead  peroxide  (PbO2) 
and  the  anode  of  spongy  metallic  lead.      These  two  plates, 

237 


238  PRACTICAL  APPLIED  ELECTEICITY 

or  "grids,"  as  they  are  called,  are  immersed  in  an  electro- 
lyte of  dilute  sulphuric  acid.  The  lead  peroxide  and  spongy 
lead  are  called  the  active  materials  of  the  cell.  They  are 
both  converted  in  lead  sulphate  (PbSO4),  which  is  insoluble, 
when  the  cell  is  being  discharged,  and  this  lead  sulphate 
is  reconverted  into  lead  peroxide  and  spongy  lead  when  the 
cell  is  being  charged. 

The  electrode  of  a  storage  cell,  which  is  the  cathode  on 
discharge,  is  called  the  positive  grid  and  the  other  electrode 
is  called  the  negative  grid. 

255.  Action   of  a   Lead   Storage   Cell   While   Discharging. — 
In  discharging  a  lead  cell,  the  electrolyte  (H2SO4)  is  split  up 
by  the  current  into  hydrogen   (H)  and  sulphion   (SO4).     The 
hydrogen    which    is    liberated    at    the    cathode    converts    the 
lead  peroxide  (PbO2)  into  lead  oxide  (PbO).     The  lead  oxide 
immediately  combines  with  a  part  of  the  electrolyte  (H2SO4), 
forming   lead   sulphate   and    water.     Lead    sulphate    (PbSO4) 
is   formed   at  the   anode  by   the   sulphion    (SO4),    combining 
with  the  spongy  lead  (Pb). 

The  lead  sulphate  which  is  formed  during  the  discharging 
process  is  more  bulky  than  the  active  materials  themselves 
and,  as  a  result,  there  is  an  expansion  in  the  plates  of  the 
cell.  There  is  also  a  decrease  in  the  density  of  the  elec- 
trolyte on  account  of  the  absorption  of  the  sulphion  (SO4) 
by  the  active  material. 

The  chemical  action  taking  place  in  the  cell  can  be  easily 
shown  by  the  equation 

Discharging  (current  from  negative  to  positive  grid) 

Positive   grid   PbO2  +  H2SO4  +  H2  =  2H2O  +  PbSO4 

Negative  grid  Pb  +  SO4  =  PbSO4 

256.  Action  of  Storage  Cell  While  Charging* — In  charging 
a  lead  storage  cell,  an  action  takes  place  which  is  just  the 
reverse  of  that   described   in   section    (255).     The   lead   sul- 
phate  (PbSO4)   on  one  grid  is  converted  back  to  lead  per- 
oxide (PbO2),  the  lead  sulphate  (PbSO4)  on  the  other  grid  is 
converted  back  to  spongy  lead  (Pb),  the  density  of  the  elec- 
trolyte   increases    and    the    volume    of    the    active    material 
decreases.     The  following  equations  will  serve  to  show  the 
chemical  action  that  takes  place  in  the  cell  when  it  is  being 
charged. 

Charging  (current  from  positive  to  negative  grid) 


STORAGE  BATTERIES  239 

Positive  grid     PbSO4  +  2H2O  +  SO4  =  2H2SO4  +  PbO2 
Negative  grid   PbSO4  +  H2  =  H2SO4  +  Pb 

257.  Storage    Battery    Grids. — Two    general    processes    are 
employed  in  the  manufacture  of  storage  battery  grids,  viz, 
the  Plante  process  and  the  Faure  process. 

258.  The     Plante     Process. — In     the    Plante    process    the 
surface  of  a  lead  plate  is  subjected  to  the  action  of  a  suitable 
acid  which  converts  the  surface  of  the  plate  into  active  mate- 
rial.   In  the  first  process  the  lead  plates  were  exposed  to  the 
action  of  dilute  sulphuric  acid,  and  the  action  was  accelerated 
by  making  the  plates  being  formed  alternately  the  anode  and 
cathode  of  the  electrolytic  cell.     The  modern  process  is  far 
superior  to  the  old  method,  the  formation  of  the  active  mate- 
rial being  brought  about  in  a  much  shorter  time  by  adding  a 
small  quantity  of  lead  dissolving  acid,  such  as  acetic  or  nitric 
acid,  and  increasing  the  area  of  the  plates  exposed  to  the 
action  of  the  acid,  by  cutting  grooves  in  their  surface. 

259.  Faure  Process. — In  the 
Faure  process  the  active  ma- 
terial is  manufactured  in  bulk 
and  introduced  by  a  mechan- 
ical process  into  openings  in 
the  lead  grids.     The  original 
process,  and  one  that  is  used 
quite  extensively  at  the  pres- 
ent time,  consisted  in  mixing 
litharge  or  a  mixture  of  lith- 
arge and  red  lead  with  dilute 
sulphuric    acid,    and    placing 
the  paste  in  suitable  support- 
ing frames,   the   combination  Fig.  201 
forming  the  grids. 

260.  Examples    of    Plante    and    Faure    Plates.— The    grids 
manufactured   by   the   Gould    Storage    Battery    Company,    as 
shown  in  Fig.  201,  are  a  good  example  of  the  modern  Plante 
plate.   Thick  plates  of  lead  of  the  proper  dimensions  are  passed 
over  rapidly  revolving  rolls  which  consist  of  a  large  number 
of  thin  disks  separated  from  each  other  by  thin  washers.    The 
action  of  these  disks  is  such  that  fins  of  lead  are  raised  upon 
the  surface  of  the  lead  plates.    Both  surfaces  of  the  plates  are 
subjected  to  the  action  of  the  spinning  rolls,  but  central  webs 


240 


PRACTICAL  APPLIED  ELECTRICITY 


Fig.  202 


and  cross-ribs  are  left  where  the  plate  is  in  no  way  changed. 

The  purpose  of  these  central  webs  and  cross-ribs  is  to  add 

conductivity  and  strength  to  the  plates. 

The  positive  grid  used  in  the  sta- 
tionary type  of  storage  cell  manu- 
factured by  the  Electric  Storage 
Battery  Company,  which  are  often 
called  "chloride"  cells,  is  shown  in 
Fig.  202.  A  casting  is  first  made 
of  lead-antimony  alloy,  with  numer- 
ous holes  in  it,  and  small  coils  of 
pure  lead  are  placed  in  these  holes. 
These  coils  of  lead  are  then  con- 
verted into  active  material  by  the 
Plante  process. 

The  'negative  grid  used  in  the 
stationary  storage  cell  of  the  Elec- 
tric Storage  Battery  Company  is 
shown  in  Fig.  203.  Two  plates  of 
pure  lead  with  numerous  holes  in 

them  are  pressed  together  over  a  block  of  active  material 

which  squeezes  out  through  the  holes.     While  the  plates  are 

still  under  pressure  they  are  riveted  together.    In  the  "exide" 

cell  made  by  the  Electric  Storage 

Battery    Company,    the    grids    are 

cast  of  a  lead-antimony  alloy  with 

a  large  number  of  small  openings 

in    them.     The    openings    in    the 

plates  that  are  to  form  the  positive 

grids  are  filled  with  a  paste  of  red 

lead  and  dilute  sulphuric  acid,  and 

the  openings  in  the  plates  that  are 

to  form  the  negative  grids  are  filled 

with  a  paste  of  litharge  and  dilute 

sulphuric  acid. 
261.       Comparison  of  Plante  and 

Faure    Plates. — The    Plante    plates 

are  more  costly  for  a  given  output 

than  the  Faure  plates.     They  are 

more  bulky,  heavier,  and  more  easily  injured  by  impurities  in 

the  electrolyte.     They  are,   however,   able  to   stand  a  more 


Fig.  203 


STOEAGE  BATTEEIES 


241 


rapid  charging  and  discharging  without  injury.  They  do  not 
lose  their  active  material  as  easily  as  the  Faure  plates.  They 
are  in  general  more  durable  and  dependable  than  the  pasted 
plates  and  have  longer  life.  The  Faure  plates  are  cheap, 
light,  and  occupy  a  small  space.  They  are  not  so  easily  dam- 
aged by  impurities  in  the  electrolyte;  but  their  efficiency  is 
less  than  the  Plante  plates  for  higher  rates  of  discharge. 

262.  Capacity  of  a  Storage  Cell. — The  unit  in  which  the 
capacity  of  a  storage  battery  is  measured  is  the  ampere-hour, 
and  the  capacity  is  usually  based  upon  the  eight-hour  dis- 
charge rate.  As  an  example,  a  200-ampere-hour  battery  would 
deliver  a  current  of  25  amperes  continuously  for  8  hours. 
Theoretically  this  same  battery  should  deliver  a  current  of 
50  amperes  for  4  hours,  or  a  current  of  12  amperes  for  16 
hours;  but  as  a  matter  of  fact  the  ampere-hour  capacity  of  a 
battery  decreases  with  an  increase  in  the  rate  of  discharge. 
The  change  in  the  capacity  of  a  battery  due  to  a  change  in 
the  discharge  fate  is  given  in  Table  No.  IX.  The  8-hour  rate 
is  taken  as  a  basis  in  figuring  the  output  at  other  rates. 


TABLE  NO.  IX 

PERCENTAGE    VARIATION    OF    THE    CAPACITY    OF    A    STORAGE 

BATTERY    DUE    TO    A    CHANGE    IN    THE    RATE 

OF  DISCHARGE 


Rate  in  hours 

Percentage  of  capacity  at  8-hour   rate 

I'lante 

Faure 

Plante    (+) 
Faure    (—  ) 

8 
7 
6 
5 

4 
3 

2 

1 

100.0 
99.0 
96.5 
93.0 
88.0 
80.0 
70.0 
55.0 

100.0 
96.0 
92.0 
86.0 
80.0 
72.0 
61.0 
40.0 

100.0 
97.0 
93.5 
89.0 
83.0 
75.0 
65.0 
50.0 

263.  The  Electrolyte. — The  electrolyte  should  be  made  of 
sulphuric  acid  made  of  sulphur  and  not  from  pyrites.  Acid 
made  from  pyrites  contains  some  iron  and  the  presence  of 
this  metal  in  the  electrolyte  is  injurious  to  the  plates.  It  is 
not  essential  that  the  electrolyte  be  chemically  pure,  but  it 
should  not  contain  any  chlorine,  nitrates,  arsenic,  mercury, 
copper,  platinum,  nitric  or  acetic  acid.  The  electrolyte  should 


242  'PRACTICAL  APPLIED  EL.ECTKICITY 

always  be  purchased  from  a  very  reliable  chemical  company 
that  will  guarantee  its  being  free  from  impurities  which  will 
be  injurious  to  the  plates  in  the  storage  battery. 

The  acid  may  be  purchased  diluted  until  the  specific  gravity 
is  of  the  desired  value  for  immediate  use  in  the  cell.  In 
some  cases,  however,  it  may  be  desirable  to  purchase  the  acid 
and  reduce  its  specific  gravity  at  the  point  where  it  is  to  be 
used.  Only  distilled  or  rain  water  should  be  used  in  diluting 
the  acid  and  the  acid  should  always  be  poured  into  the  water. 
There  will  be  considerable  heat  liberated  and  the  solution 
should  be  allowed  to  cool  before  a  determination  of  the 
specific  gravity  is  made  as  there  is  quite  a  change  in  the 
specific  gravity  due  to  a  change  in  the  temperature  of  the 
electrolyte.  The  density  of  the  acid  to  use  will  of  course 
depend  upon  the  kind  of  cell  it  is  to  be  used  in,  the  ampere- 
hour  capacity  of  the  cell,  its  rate  of  discharge  and  charge,  etc. 
The  density  that  will  give  the  best  results  for  any  particular 
cell  is,  in  the  majority  of  cases,  specified  by  the  makers. 

264.  Density  and  the  Hydrometer. — The  density 
of  any  substance  is  the  ratio  of  the  weights  of 
equal  volumes  of  the  substance  and  water.  Thus, 
if  the  specific  gravity  of  a  certain  quantity  of 
sulphuric  acid  is  1.25,  it  means  that  a  certain 
volume  of  the  acid  will  weigh  1.25  times  as  much 
as  the  same  volume  of  pure  water. 

The  hydrometer  is  an  instrument  for  measuring 
the  density  of  liquid.    It  is  placed  in  the  liquid  and 
is  so  constructed  that  a  portion  of  it  projects  above 
the  surface  of  the  liquid.     The  amount  projecting 
FigT204      wiU   vary    with    the    density    of   the    liquid    and    a 
suitable    scale    attached    or    marked    on    the    up- 
wardly projecting  portion  will  afford  a  means  of  determining 
the  density  of  the  liquid  direct  from  the  scale  reading.     The 
reading  is  taken  at  the  surface  of  the  liquid.    The  outline  of 
a  hydrometer,  is  shown  in  Fig.  204.    A  small  quantity  of  lead 
shot  in  the  lower  portion  gives  the  instrument  the  required 
weight  and  serves  to  hold  it  always  in  an  upright  position. 

265.  Containing  Vessel  and  Separators.— There  are  a  num- 
ber of  different  kinds  of  containing  vessels  for  the  plates  and 
electrolyte  of  a  storage  cell,  and  perhaps  the  most  important 
of  these  are  those  made  of  rubber,  glass,  and  lead-lined 


STORAGE  BATTERIES 


243 


wooden  tanks.  The  rubber  containing  vessel  is  used  in  the 
construction  of  portable  cells  because  it  will  stand  more  abuse 
than  glass  and  is  much  lighter.  Glass  containing  vessels  are 
used  for  stationary  cells  of  moderate  capacity.  The  lead-lined 
wooden  tanks  are  used  for  very  large  cells  as  they  are 
stronger  than  either  the  glass  or  the  rubber  and  the  increase 
in  weight  makes  no  great  difference. 

When  the  plates  are  placed  in 
the  containing  vessels,  they  are 
positive  and  negative  alternately. 
This  results  in  adjacent  plates  be- 
ing of  opposite  polarity  and  some 
means  must  be  provided  for  sepa- 
rating them.  Perforated  rubber 
sheets  are  used  in  the  smaller 
cells,  rubber  sheets  and  thin 
sheets  of  porous  wood  in  medium 
size  cells,  and  glass  rods  in  the 
larger  cells.  The  interior  of  a 
cell  is  shown  in  Fig.  205. 

266.  Sulphation. — In  the  section 
describing  the  chemical  action  of 
the  storage  battery,  it  was  men- 
tioned that  lead  sulphate  was 
formed  when  the  cell  was  dis- 
charged. This  lead  sulphate  is 
insoluble  in  sulphuric  acid  and  oc- 
cupies a  larger  volume  than  the 
pure  lead  or  lead  peroxide  which 
forms  it,  and  it  is  a  non-conductor. 

In  discharging  a  storage  battery,  it  should  not"  be  allowed  to 
go  beyond  a  point  where  a  small  part  of  the  active  material 
is  converted  into  lead  sulphate.  If  the  battery  be  over  dis- 
charged there  will  be  an  excessive  amount  of  the  sulphate 
formed  or  as  it  is  termed,  an  oversulphation. 

The  presence  of  the  excessive  amount  of  sulphate  results 
in  the  surface  of  the  plates  being  covered  with  white  crystals 
and  the  pores  of  the  plates  are  closed  up  due  to  the  increase 
in  volume.  The  surface  of  the  active  material  exposed  is,  as  a 
result,  decreased  due  to  the  presence  of  the  crystals,  and  the 
increase  in  volume  will  cause  the  active  material  to  be  loos- 


Fig.  205 


244  PKACTICAL  APPLIED  ELECTKICITY 

ened  from  the  grid,  or  it  may  result  in  the  plate  being  bent 
out  of  shape,  which  will  result,  in  some  cases,  in  the  plates 
being  fractured  and  the  active  material  falling  to  the  bottom 
of  the  cell  as  sediment.  The  distortion  of  the  plates  is  known 
as  buckling.  A  high  discharge  rate  results  in  a  greater 
expansion  than  a  low  rate  and  the  active  material  is  more 
likely  to  fall  away  when  the  battery  is  being  discharged  at  a 
high  rate  than  it  is  when  discharged  at  a  low  rate. 

267.  Battery  Troubles  and  Their  Remedies. — The  following 
troubles  are  perhaps  the  most  important  ones  encountered  in 
the  operation  of  a  storage  battery: 

(A)  Loss  of  capacity. 

(B)  Loss  of  voltage. 

(C)  Corrosion  of  electrodes. 

(D)  Buckling  of  plates. 

(E)  Shedding  active  material. 

268.  (A)    Loss  of  Capacity. — The  loss  of  capacity  may  be 
due  to  any  one  or  all  of  the  following  causes:      (a)   sulpha- 
tion;    (b)  loss  of  active  material;    (c)  loss  of  electrolyte;   (d) 
sulphate  between  grid  and  the  active  material;  and  (e)  con- 
traction of  active  material  on  spongy  lead  plate. 

(a)  The  causes  of  sulphation  have  already  been  discussed 
but  the  means  of  treating  sulphated  plates  will  be  given  here. 
To  remove  the  sulphate,  charge  the  battery  at  as  high  a  rate  as 
possible  without  causing  the  temperature  of  the  cell  to  exceed 
110°  Fahrenheit  until  the  plates  gas  very  freely,  then  reduce 
the  rate  to  the  normal  8-hour   rate  and   continue  until  the 
plates  again  begin  to  gas.     Then  reduce  to  half  the  8-hour 
rate  and  continue  until  the  plates  gas.    Now  give  the  battery 
a  partial  discharge  and  then  recharge  as  just  described.    This 
cycle  of  operations  may  have  to  be  repeated  a  number  of  times 
before  all  the  sulphate  is  removed. 

(b)  Loss  of  active  material  is  usually  due  to  the  plates  not 
being  worked  under  normal  conditions;  if  this  is  not  the  case, 
the  plates  are  poorly  designed.     This  loss  is  due  chiefly  to 
rapid    charge   and    discharge,    sulphation,    and    a   long   over- 
charge. 

(c)  Loss  of  electrolyte  due  to  evaporation  may  cause  the 
surface  of  the  liquid  to  fall  below  the  upper  edge  of  the  plates. 
The  remedy  is  obvious. 

(d)  In  the  Faure  type  of  plates,  sulphate  may  form  between 


STORAGE  BATTEEIES  245 

the  active  material  and  the  supporting  grid,  which  greatly 
increases  the  electrical  resistance  of  the  cell  and  decreases 
the  area  of  the  active  material. 

(e)  The  active  material  on  the  spongy-lead  electrode  will 
contract  and  such  shrinkage  will  close  up  the  pores  and 
greatly  reduce  the  active  surface.  There  are  methods  of 
preventing  this  contraction  in  use  by  several  companies.  If 
you  think  your  battery  trouble  is  due  to  this  cause,  it  would 
be  best  for  you  to  get  advice  from  the  manufacturers  of  the 
battery. 

269.  (B)    Loss  of  Voltage. — The  causes  of  loss  in  voltage 
are  the  same  as  those  resulting  in  a  loss  of  capacity  and  the 
treatment  of  the  cell  for  the  two  conditions  is  identical. 

270.  (C)  Corrosion  of  Plates. — The  corrosion  of  the  plates 
is  usually  due  to  the  presence  of  some  injurious  impurities  in 
the  electrolyte  and  the  only  remedy  is  to  change  the  electrolyte. 

271.  (D)     Buckling  of  Plates. — Any  condition  of  operation 
of  the  cell  which  will  result  in  an  unequal  chemical  action 
over    the   surface    of   the    plates    will    result    in    an    unequal 
expansion  of  the  active  material  and  hence,  a  tendency  for 
the  plate  to  expand  more  in  some  spots  than  others.     These 
stresses  which  are  set  up  in  the  plates  relieve  themselves  by 
changing  the  form  of  the  plates.     Buckling  is  usually  due  to 
improper  design  and   cannot  be  overcome  except  by  recon- 
struction. 

272.  (E)    Shedding   of  Active    Material. — When  the  active 
material  on  the  plates  drops  off  more  rapidly  than  it  should — 
which  is  indicated  by  the  rapid  accumulation  of  sediment  in 
the  bottom  of  the  cell— the  cell  should  be  worked  at  a  low 
rate   of  discharge,   never   being   discharged   below   1.75   volts 
and  never  being  charged  above  2.4  volts. 

273.  Management  of  a  Storage  Battery. — There  are  a  few 
important  rules  that  one  should  always  bear  in  mind  in  the 
care  of  a  lead  storage  battery. 

(a)  Always  use  a  pure  electrolyte. 

(b)  Never  allow  the  surface  of  the  electrolyte  to  fall  below 
the  upper  edge  of  the  plates. 

(c)  Always  maintain  the  specific  gravity  at  the  value  speci- 
fied by  the  manufacturers. 

(d)  Keep  cells  well  cleaned,  never  allow  sediment  to  rise 
until  it  is  in  contact  with  the  lower  edge  of  the  plates. 


246  PRACTICAL  APPLIED  ELECTKICITY 

(e)  Keep  all  separators  in  place  so  that  there  is  no  danger 
of  the  plates  coming  in  contact  with  each  other  and  shorting 
the  cell. 

(f)  Keep    cells   well   insulated   by   placing   them    in   trays 
that  are  supported  on  insulators. 

(g)  Inspect  all  cells  occasionally  for  leaks  in  the  contain- 
ing vessel  and  either  replace  the  broken  vessel  by  a  new  one 
or  repair  it  immediately. 

(h)  Always  charge  the  battery  as  soon  as  possible  after 
discharge. 

(i)  Never  overcharge  the  battery  or  after  the  negative 
plates  begin  to  gas,  except  as  stated  in  section  (268). 

(j)  Never  allow  the  battery  to"  discharge  below  1.75  volts 
at  the  normal  rate  of  discharge  and  1.6  volts  when  discharg- 
ing at  the  1-hour  rate. 

(k)  Watch  the  plates  for  signs  of  sulphation  and  if  any 
sulphate  appears,  treat  them  immediately  as  described  in 
section  (268). 

(I)  Always  keep  the  temperature  of  the  battery  below  110° 
Fahrenheit. 

(m)  Give  the  battery  a  prolonged  over-charge  occasionally 
until  free  gassing  of  the  negative  plate  has  continued  for  one 
hour. 

274.  To  Put  a  Cell  Out  of  Service. — When  a  cell  is  to  be 
out  of  service  for  several  months  or  for  an  indefinite  period,  it 
can  be  treated  as  follows  and  will  then  need  no  attention  until 
it  is  desired  to  be  used  again.     Fully  charge  the  cell,  then 
discharge  it  for  about  two  hours  at  the  normal  rate.    After  the 
cell  has  been  discharged,  draw  off  the  electrolyte  and  fill  the 
vessel  with  distilled  water.     Now  again  discharge  the  cell  at 
the  normal  rate  until  its  terminals  must  be  shorted  to  produce 
the  discharge  current.     Pour  out  the  water  and  again  fill  the 
cells,  allowing  them  to  stand  for  a  day  or  so  when  this  water 
should  be  drawn  off  and  the  plates  allowed  to  dry.    To  put  the 
cell  back  in  service,  the  electrolyte  should  be  placed  in  the 
cell  and  the  cell  should  be  given  a  prolonged  over-charge. 

275.  Non-Lead  Storage  Cells. — Almost  any  primary  cell  may 
be  made  to  act  more  or   less  as  a   secondary   cell;    as,   for 
example,  the  gravity  cell  may  be  charged  by  passing  a  current 
through  it  opposite  to  the  direction  the  current  passes  through 
the  cell  on  discharge.     Quite  a  number  of  cells  have  been 


STORAGE  BATTERIES  247 

devised  in  which  metals  other  than  lead  is  used  for  one  or  both 
of  the  plates.  Reynier  made  a  cell  in  which  the  negative  plate 
was  composed  of  zinc  instead  of  lead,  and  this  zinc  was  con- 
verted into  zinc  sulphate  when  the  cell  was  discharging,  which 
dissolved  in  the  electrolyte.  The  electromotive  force  of  this 
cell  was  considerably  higher  than  that  of  the  ordinary  lead 
cell  and  it  was  quite  a  bit  lighter,  since  for  the  storage  of  a 
given  amount  of  energy  the  weight  of  zinc  required  is  much 
less  than  that  of  the  equivalent  lead.  This  cell,  however,  is 
not  very  satisfactory  in  operation,  since  there  are  trees  of  zinc 
formed  on  the  negative  plate  during  the  process  of  charging, 
and  these  trees  are  likely  to  extend  out  from  the  negative 
plate  a  sufficient  distance  to  short-circuit  the  cell.  There  is 
also  a  difference  in  the  density  of  the  electrolyte  at  the  top 
and  the  bottom  of  the  cell,  which  results  in  the  action  on  the 
plates  not  being  uniform.  This  difficulty  was  overcome  to  a 
certain  extent  by  placing  the  plates  in  a  horizontal  instead  of 
in  a  vertical  position.  Where  the  plates  are  horizontal,  however, 
there  is  an  accumulation  of  the  liberated  gases  upon  the  sur- 
face of  the  plates  and,  as  a  result,  an  increase  in  the  internal 
resistance  of  the  cell. 

Waddell  and  Entz  constructed  a  storage  cell  in  which 
copper  and  zinc  are  used  as  the  plates  and  the  electrolyte  is 
an  alkali  solution.  When  the  cell  is  discharged,  the  positive 
plate  consists  of  porous  copper  and  on  charging,  the  elec- 
trolyte is  decomposed,  metallic  zinc  is  deposited  on  the 
negative  plate,  the  porous  copper  forming  the  positive  plate  is 
oxidized,  and  the  liquid  forming  the  electrolyte  is  converted 
into  a  solution  of  caustic  potash.  The  electromotive  force  of 
this  cell  is  very  low,  it  being  only  about  .7  volt  and,  as  a 
result,  approximately  three  times  as  many  cells  must  be  used 
to  give  a  given  voltage  as  would  be  required  if  the  lead  cells 
were  used.  This  is  a  very  serious  objection  to  this  particular 
cell  or  to  any  other  low  voltage  cell. 

276.  Edison  Storage  Battery. — In  the  Edison  battery  the 
active  materials  are  oxides  of  nickel  and  iron,  respectively,  in 
the  positive  and  the  negative  electrodes,  the  electrolyte  being 
a  solution  of  caustic  potash  in  water.  The  retaining  vessels 
for  these  cells  are  made  from  sheet  steel,  their  walls  being 
corrugated  to  add  strength  with  a  minimum  weight.  The 
completed  can  is  nickel-plated,  which  protects  the  steel  from 


248 


PEACTICAL  APPLIED  ELECTRICITY 


rust  and  at  the  same  time  adds  to  the  appearance  of  the  cell. 
There  are  a  number  of  different  types  of  Edison  cells  on  the 
market,  but  they  differ  only  in  the  number  of  plates  they 
contain.  Each  positive  plate  consists  of  a  grid  of  nickel-plated 
steel  holding  30  tubes  filled  with  the  active  material,  in  two 
rows  of  15  tubes  each,  as  shown  in  Fig.  206.  The  tubes  are 
made  of  very  thin  sheet  steel,  perforated  and  nickel-plated. 
Each  tube  is  reinforced  and  protected  by  small  ferrules,  eight 
in  number.  These  ferrules  prevent  expansion  and  thereby 
retain  perfect  internal  contact  with  the  active  material  at  all 
times.  The  active  material  in  the  tubes  is  interspersed  with 
thin  layers  of  pure  metallic  nickel  in  the  form  of  leaves  or 
flakes.  The  pure  nickel  flake  that  is  used  is  manufactured 
by  a  special  electrochemical  process. 

Each  negative  plate  comprises  24 
flat  rectangular  pockets  supported 
in  three  horizontal  rows  in  nickel- 
plated  steel  grids,  as  shown  in  Fig. 
207.  The  pockets  are  made  of  thin 
nickel-plated  steel,  perforated  with 
fine  holes,  each  pocket  being  filled 
with  an  oxide  of  iron  very  similar 
to  what  is  called  iron  rust.  In  the 
construction  of  the  negative  plate 
each  pocket  is  subjected  to  a  very 
high  pressure,  so  that  it  becomes 
practically  integral  with  the  sup- 
porting grid. 

The  positive  and  the  negative 
plates  are  hung  alternately  on  two 
connecting  rods,  the  positive  plates 
being  electrically  connected  to  one 

rod  and  the  negative  plates  to  the  other.  The  plates  are 
properly  distanced  on  these  rods  by  nickel-plated  steel' spac- 
ing washers,  and  are  held  firmly  in  place  and  contact  by 
nuts  screwed  on  both  ends.  In  assembling  the  plates  a 
specially  shaped  lug  is  placed  in  the  center  of  each  of  the 
connecting  rods,  as  shown  in  Fig.  207.  These  rods  project 
upward  and  are  of  sufficient  length  to  protrude  through  open- 
ings in  the  top  of  the  containing  can,  thus  forming  the  ter- 
minals of  the  cell.  There  is  always  one  more  negative  plate 


Fig.  206 


STORAGE  BATTEEIES 


349 


in  the  Edison  cell  than  there  are  positive,  just  as  there  is  in 
the  lead  cell,  which  results  in  both  outside  plates  being  nega- 
tive. Special  insulators  are  used  in  separating  the  plates  and 
preventing  them  from  coming  into  contact  with  the  containing 
can. 

277.  Chemistry  of  the  Edison 
Storage  Battery. — Starting  with  the 
oxide  of  iron  in  the  negative,  green 
nickel  hydrate  in  the  positive,  and 
potassium  hydrate  in  solution,  the 
first  charging  of  a  cell  reduces  the 
iron  oxide  to  metallic  iron  while  con- 
verting the  nickel  hydrate  to  a  very 
high  oxide,  black  in  color.  On  dis- 
charge, the  metallic  iron  goes  back 
to  iron  oxide  and  the  high  nickel 
oxide  goes  to  a  lower  oxide  but  not 
to  its  original  form  of  green  hydrate. 
On  every  cycle  thereafter,  the  nega- 
tive charges  to  metallic  iron  and  dis- 
charges to  iron  oxide,  while  the  posi- 
tive charges  to  a  high  nickel  oxide. 
Current  passing  in  either  direction 
(charge  or  discharge)  decomposes 
the  potassium  hydrate  of  the  elec- 
trolyte, and  the  oxidation  and  reduc- 
tions at  the  electrodes  are  brought 
about  by  the  action  of  its  elements. 
An  amount  of  potassium  hydrate 
equal  to  that  decomposed  is  always 

re-formed  at  one  of  the  electrodes  by  a  secondary  chemical 
reaction,  and  consequently  there  is  none  of  it  lost  and  its 
density  remains  constant. 

The  eventual  result  of  charging,  therefore,  is  a  transference 
of  oxygen  from  the  iron  to  the  nickel  electrode,  and  that  of 
discharging  is  a  transference  back  again.  This  is  why  the 
"Edison"  is  sometimes  called  an  oxygen  lift  cell. 

When  both  electrodes  become  fully  charged,  the  elements 
of  the  decomposed  potassium  hydrate  can  no  longer  act  on 
them,  but  instead  they  react  to  produce  hydrogen  and  oxy- 
gen— the  elements  of  water  which  are  given  off  as  a  gas. 


Fig.  207 


£50  PEACTICAL  APPLIED  ELECTEICITY 

Nickel  plates  in  the  positive  and  mercury  in  the  negative 
do  not  take  part  in  the  chemical  reaction  but  are  used  solely 
to  bring  the  particles  of  active  material  into  good  electrical 
contact  with  the  conducting  support. 

278.  Care  of  an  Edison  Storage  Battery. — Edison  storage 
batteries  are  shipped  in  a  discharged  condition,  and  should 
be  given  a  long  initial  charge  before  being  put  into  service. 
The  duration  of  this  first  charge  should  be  about  15  hours  at 
the  normal  rate,  and  it  is  recommended  by  the  company  that 
this  overcharge  be  repeated  once  every  two  weeks  for  the 
first  two  months,  when  the  battery  is  in  constant  service.  If, 
however,  the  battery  is  not  in  constant  service,  it  should  be 
given  a  long  charge  after  every  12  complete  charges  and  dis- 
charges until  five  long  charges  have  been  put  in.  This  con- 
stitutes what  might  be  called  the  forming  process,  and  it  is 
advisable  to  repeat  the  long  charges  about  every  two  months 
throughout  the  life  of  the  battery. 

In  charging  an  Edison  battery,  the  seven-hour  charge  at  the 
normal  rate  is  arbitrarily  chosen  as  normal  for  the  reason 
that  a  battery  will  retain  good  efficiency  up  to  this  point. 
This  rate,  however,  is  not  fixed  and  may  be  varied  at  will,  the 
highest  practical  output  being  reached  on  a  ten-hour  charge, 
which  gives  a  maximum  efficiency  of  about  30  per  cent  above 
normal  rated  output.  Overcharging  is  in  no  way  harmful, 
provided  the  temperature  is  not  allowed  to  exceed  100°  Fahren- 
heit at  any  time  while  charging.  The  cells  must  be  frequently 
filled  when  they  are  overcharged  and  overcharging  means  a 
waste  of  energy.  The  evaporation  must  be  replaced  with  pure 
distilled  water,  and  under  no  circumstances  use  any  acid.  The 
solution  should  never  be  allowed  to  go  below  the  tops  of  the 
plates,  the  proper  height  being  one-half  inch  above  the  plates. 
It  is  always  advisable  to  fill  the  battery  before  charge  as  in 
the  process  of  charging  the  liquid  is  raised  to  a  false  level. 

The  electrolyte— which  is  a  21  per  cent  solution  of  potash 
(KOH) — in  a  battery  in  constant  service,  being  charged  and 
discharged  each  day,  should  be  renewed  once  every  eight  or 
nine  months. 

279.  Commercial  Applications  of  Storage  Batteries. — The 
following  list  gives  the  principal  uses  to  which  the  storage 
battery  may  be  placed: 

(a)     To  supply  energy  to  portable  electrical  apparatus. 


STORAGE  BATTERIES  251 

(b)  As  a  source  of  constant  potential  and  current  in  elec- 
trical laboratories. 

(c)  As  a  source  of  energy  in  telephone  and  telegraph  work. 

(d)  To  supply  energy  for  train-lighting. 

(e)  To  reduce  the  fluctuations  in  the  load  on  a  generator, 
by  operating  the  battery  and  the  generator  in  parallel. 

(f)  To  supply  energy  during  certain  hours  when  the  load 
on  a  power  plant  is  low  and  thus  allow  the  generator  to  be 
shut  down. 

(g)  To  supply  energy  and  aid  the  generator  in  carrying  the 
maximum  load  (peak)  which  usually  lasts  only  a  few  hours. 

(h)  To  change  froni  a  high  to  a  low  voltage  by  charging 
the  cells  in  series  and  discharging  them  in  parallel,  or  vice 
versa. 

(i)  As  a  means  of  subdividing  the  voltage  of  a  main  gen- 
erator, enabling  it  to  supply  energy  to  a  multi-voltage  system. 

(j)  To  supply  energy  for  electrically  driven  vehicles  and 
boats. 

280.  Portable   Storage    Batteries. — Practically   all   the   bat- 
tery companies  manufacture  a  portable  form  of  storage  cell. 
These  cells  are  usually  constructed  so  that  they  will  be  as 
light  and   compact   as    possible,   and   mounted   in   a    suitable 
containing  case  outside  the  one  holding  the  electrolyte,  which 
gives  ample  protection  to  the  cell  and   affords   a  means  of 
easily  carrying  the   cell,  by  providing  this   outer   case   with 
some  kind  of  a  handle.     The  number  of  cells  mounted  in  each 
outer  containing  case  may  vary  depending  upon  the  particular 
use  to  which  the  battery  is  to  be  placed. 

The  great  objection  to  portable  storage  cells  is  their  great 
weight  and  this  is  almost  prohibitive  of  their  general  use. 
Portable  cells  are  used  in  operating  small  lighting  systems 
such  as  occur  on  automobiles  and  launches,  in  operating  spark 
coils  for  gas  engines,  in  operating  small  lamps  and  motors  for 
various  special  purposes,  etc. 

281.  Storage     Batteries    in     Electrical     Laboratories. — The 
storage  battery  is  a  valuable  source  of  energy  in  electrical 
laboratories,  as  the  regulation  of  the  voltage  and  the  current 
can  be  accomplished  by  means  of  the  adjustment  of  a  simple 
rheostat  of  some  kind.     The  voltage  of  the  battery  can  be 
changed  by  changing  the  grouping  of  the  cells,  a  maximum 
voltage  being  obtained  when  they  are  all  connected  in  series 


PEACTICAL  APPLIED  ELECTEICITY 

and  a  minimum  voltage  when  they  are  all  connected  in 
parallel.  When  a  large  current  is  wanted  at  a  low  voltage, 
it  can  be  more  easily  obtained  and  at  a  less  expenditure  of 
energy  than  if  the  same  current  were  taken  from  a  higher 
voltage.  The  connections  of  jg^arging  ar*(d  discharging  board 
are  shown  in  Fig.  209. 

282.  Storage  Batteries  in  Telephone  and  Telegraph  Work. 
— Storage  batteries  have  come  into  general  use  in  telephone 
exchanges   since  the  introduction  of  what  is  known  as  the 
common-battery    telephone    system.     In   this    system   instead 
of  each   subscriber  having  a  battery   of  two   or   more   cells 
placed  in  his  instrument,  these  batteries  are  all  combined  in 
one  large  battery  located  at  the  central  office,  and  each  sub- 
scriber's   line    is    supplied    with    current    from   this    main    or 
central  battery.     The  storage  battery  is  preferable  for  this 
main  battery  for  the   following   reasons:     Lower  first   cost; 
smaller  space  required;  lower  internal  resistance;   more  con- 
stant electromotive  force;  rapidity  of  recharge,  and  low  cost 
of  maintenance.     Two  batteries  are   usually  placed   in  each 
exchange  so  that  one  can  be  on  charge  and  held  in  reserve 
while  the  other  battery  is  in  use. 

In  telegraph  work  the  storage  battery  may  be  used  alone 
or  in  combination  with  small  generators  in  supplying  current 
to  operate  the  telegraph  instruments. 

283.  Storage    Batteries  for   Train    Lighting. — The   simplest 
method  of  lighting  a  train  by  electricity  is  to  install  a  small 
dynamo  on  the  locomotive,  which  may  be  driven  by  a  small 
steam  engine  or  turbine.    With  this  arrangement  there  is  the 
objection  that  the  cars  must  be  illuminated  by  some  other 
means  when  the  locomotive  is  uncoupled.    This  has  led  to  the 
storage-battery  system  of  supplying  energy  to  each  car  sepa- 
rately even  though  it  be  disconnected  from  the  main  train. 
The  battery  is  so  connected  that  it  is  being  charged  when 
connected  to  the  main  generator  leads,  provided  the  voltage 
between   the   generator   leads   is   greater   than   the   terminal 
voltage  of  the  battery.     When  the  generator  voltage   drops 
below  a  certain  point,  due  to  any  cause,  the  battery  discharges 
and  the  lamps  continue  to  burn  just  as  though  the  generator 
were  operating.     The  connections  of  the  battery  lamps  and 
the  generator  are  controlled  by  a  specially  constructed  switch 
that  is  automatically  operated.     In  some  cases  a  small  gen- 


STOEAGE  3ATTEKIE3  253 

erator  is  mounted  on  each  car  and  driven  by  a  belt  that  passes 
over  a  pulley  on  one  of  the  axles.  The  generator  in  this 
system  is  inoperative  when  the  car  is  at  rest  and  the  battery 
must  necessarily  carry  the  load. 

284.  Storage  Battery  and  <d«||erator  in  Parallel.— Often  the 
load  a  generator  is  called  upon  to  carry  fluctuates  in  value 
and   in   a  great  many   cases   it   is   desired   that  the  voltage 
between  the  lines  remain  as  near  constant  in  value  as  pos- 
sible.    With  a  fluctuating  load  there  would  necessarily  be  a 
change  in  line  voltage  due  to  a  change  in  the  value  of  the 
copper  drop  unless  there  was  a  change  in  the  voltage  at  the 

generator    terminals    that 

+  would  counteract  the  cop- 

I    +     1  per  drop.     By   connecting 

^          a  battery  in  parallel  with 

Battery  ;  Load          the  generator,  as  shown  in 

-=c-       | Fig.    208,    the    battery 

-3-^ — t  charges  when  the  load  is 

Fig.  208  light    and    will    discharge 

when  the  load  is  of  such  a 

value  that  the  voltage  between  the  line  wires  is  less  than  the 
battery  voltage.  As  a  result,  the  copper  drop  in  the  leads 
from  the  generator  remains  nearer  constant  in  value  and 
there  is  a  smaller  fluctuation  in  the  value  of  the  line  voltage 
due  to  a  change  in  load  than  there  would  be  if  no  battery 
were  used. 

285.  Storage    Battery    to    Supply    Energy    During    Certain 
Hours. — In  a  great  many  generating  plants,  the  energy  the 
generator  is  called  upon  to  supply  during  certain  periods  is  so 
small  that  it  would  be  poor  economy  to  operate  the  generator 
on  so  small  a  load.     A  storage  battery  can  be  installed  of 
ample  capacity  to  carry  the  load  during  this  period  and  the 
plant  entirely  shut  down.     The  output  of  a  generating  plant 
is  represented  by  curve  (A),  Fig.  210.     It  will  be  seen  from 
this  curve  that  the  load  carried  by  the  generator  from  about 
6  P.M.  to  5  A.M.  is  very  small.    By  installing  a  storage  battery 
having  the  required  k.w.  hours'  capacity,  the  generator  can  be 
shut  down  during  part  of  the  night. 

286.  Storage  Batteries  to  Aid   Generators  in  Carrying  the 
Maximum  Load. — Assuming  the  load  on  a  generating  plant  is 
similar  to  that  shown  by  curve    (B)   in   Fig.   210,   sufficient 


254 


PBACTICAL  APPLIED  ELECTEICITY 


generator  capacity  must  be  installed  to  take  care  of  the 
maximum  load  at  any  time  without  exceeding  the  allowable 
overload  capacity  of  the  generators.  This  would  result  in  a 
large  part  of  the  equipment  being  practically  idle  during  the 
greater  portion  of  the  day,  or  a  part  of  the  machinery  would 
represent  an  investment  from  which  there  would  be  propor- 
tionally a  small  income.  By  installing  a  storage  battery,  the 


Ammeter 


Battery  \ 
Rhoestat 

Circuit-^ 
BreaKer 


Voltmeter 

Voltmeter 
Switch 

Series 
Parallel 
Switches 

Battery 
Switch 


Fig.  209 


generator  capacity  can  be  reduced,  the  battery  being  charged 
when  the  load  on  the  plant  is  light  and  discharged  in  parallel 
with  the  generators  when  the  load  exceeds  the  capacity  of 
the  generators.  The  shaded  portion  of  the  curve  in  Fig.  210 
represents  what  is  called  the  peak  of  the  load. 

287.  Storage  Batteries  Used  in  Changing  Voltage. — The 
line  voltage  available  in  a  great  many  cases  is  either  too  high 
or  too  low  for  a  given  purpose  and  some  means  must  be 
employed  for  changing  its  value.  An  easy  means  of  doing  this 


STORAGE  BATTERIES 


255 


is  to  use  a  number  of  storage  cells  and  have  them  so  arranged 
that  they  may  be  readily  changed  from  any  connection  to  an- 
other. Thus,  if  it  is  desired  to  reduce  the  voltage,  the  cells 


1 

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Time  in 

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Midnight                     Noon                   Midnight 
Fig.  210 

L, 


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no 


no 


of  a  battery  may  be  charged  in  series  and  then  connected  in 
a  number  of  groups  and  these  groups  in  turn  connected  in 
parallel.  If  it  is  desired  to  raise  the  voltage,  the  cells  should 
be  charged  in  parallel  and  then  connected  in  series  for 
discharge. 

288.  Storage  Batteries 
Used  in  Subdividing  Voltage 
of    a    Generator. — The    con- 
nections of  a  battery  for  di- 
viding the  voltage  of  a  gen- 
erator   are    shown    in    Fig. 
211.     Supposing  the  genera- 
tor   (G)    is    a    220-volt    ma- 
chine and   it  is   desired   to  Fig-.  211 
obtain  energy  from  it  at  110 

volts.  This  can  be  accomplished  by  connecting  the  battery 
(B),  which  should  have  a  voltage  of  about  220  volts,  across 
the  leads  from  the  main  generator  and  connecting  a  lead  (N) 
to  the  center  of  the  battery.  With  this  connection  there  will 
be  a  110-volt  pressure  between  each  outside  lead  and  the 
lead  (N). 

289.  Storage    Batteries  to    Supply    Energy   for    Electrically 
Driven  Vehicles  and   Boats.— The  storage  battery  is  growing 


256 


PEACTICAL  APPLIED  ELECTRICITY 


in  favor  as  a  means  of  supplying  energy  to  vehicles,  such  as 
pleasure  automobiles,  heavy  trucks,  and  street  cars;  and  it  is 
also  quite  extensively  used  in  small  pleasure  boats  and  sub- 
marines. The  battery  is  connected  to  the  motors  through 


Fig.  212 

specially  constructed  controllers,  so  arranged  that  the  cells 
are  grouped  to  give  a  low  impressed  voltage  on  starting  and 
as  the  controller  is  advanced  to  successive  positions,  the 
connections  of  the  various  cells  are  changed,  all  being  con- 
nected in  series  when  the  controller  handle  is  at  its  final 
position.  A  tray  of  six  cells,  as  used  in  an  electric  automobile, 
is  shown  in  Fig.  212. 


CHAPTEE  XIII 

DISTRIBUTION    AND   OPERATION 

290.  Systems   of    Distribution. — The    power    output    of    an 
electrical  generator  at  any  instant  is  equal  to  the  product  of 
the  terminal  voltage  of  the  machine  and  the  current  supplied 
by  the  machine.     With  a  change  in  output  there  must  be  a 
change  in  the  value  of  this  product  and  necessarily  a  change 
in  the  value  of  either  the  current  or  voltage,  or  both.     When 
the  power  output  of  the  generator  changes  due  to  a  change 
in  the  value   of  the  current,  the   machine   is   said  to   be   a 

constant-voltage    machine, 
and    the    method    employed 

*••'  *          Li-  in   supplying  energy  to  the 

M)  QQQQ  circuit  connected  to  the  ma- 
chine is  called  a  constant- 
voltage,  or  parallel  system 
of  distribution.  If  the  out- 
put of  the  machine  changes 
due  to  a  change  in  the  ter- 
minal voltage,  the  current  remaining  constant,  the  method 
employed  in  supplying  energy  to  the  circuit  connected  to  the 
machine  is  called  constant-current,  or  series  system  of  dis- 
tribution. 

291.  Constant-Voltage    Distribution. — In    the    constant-volt- 
age, or  parallel  system  of  distribution,  the  various  devices  that 
are    being    supplied    with    energy   are    connected    in    parallel 
across  the  two  lines  leading  to  the  terminals  of  the  generator. 
A  motor  (M)  and  a  number  of  lamps  (L)  are  shown  connected 
in  parallel  to  the  terminals  of  the  generator    (G),  Fig.  213. 
With  a  change  in  the  number  of  lamps  or  motors  connected, 
there  will  be  a  change  in  the  value  of  the  total  resistance 
between  the  two  leads  (Li)  and  (L2)  and,  as  a  result,  a  change 
in  the  value  of  the  current  output  of  the  machine.     Thus,  for 

257 


258  PRACTICAL  APPLIED  ELECTRICITY 

example,  if  the  generator  is  connected  to  ten  incandescent 
lamps  each  having  a  hot  resistance  of  220  ohms,  there  will 
be  a  total  resistance  of  (220  -r-  10)  or  22  ohms  between  the 
leads,  and  if  the  voltage  of  the  machine  is  110  volts,  there 
will  be  a  current  of  5  amperes  supplied  by  the  machine.  Now 
if  5  of  the  lamps  are  disconnected,  the  resistance  between  the 
leads  will  be  increased  as  the  number  of  paths  in  parallel  has 
been  decreased,  and  it  will  be  equal  to  (220-7-5)  or  44  ohms. 
The  current  supplied  by  the  generator  in  this  case  will  be 
2.5  amperes,  the  voltage  remaining  constant.  When  more 
than  ten  lamps  are  connected,  the  combined  resistance  will 
be  less  than  the  resistance  of  the  ten  and,  as  a  result,  the 
current  supplied  by  the  generator  will  increase,  which  results 
in  an  increase  in  the  power  output,  it  being  equal  to  (E  X  I). 

292.      Constant-Current 

Arc  Lamps  Distribution. — In    the    con- 

~  stant-current,    or    series 

system  of  distribution,  the 
various  devices  that  are 
being  supplied  with  ener- 
gy are  connected  in  series 
to  the  terminals  of  the 
generator.  A  number  of 
Fig.  214  arc  lamps  and  a  motor 

(M)   are  shown  connected 

in  series  in  Fig.  214,  and  the  combination  connected  to  the 
generator  (G).  If  there  is  a  change  in  the  number  of  lamps 
or  motors  connected  in  such  a  circuit  there  will  be  a  change 
in  the  value  of  the  resistance  of  the  circuit,  and  since  the 
construction  of  the  generator  (G)  is  such  that  it  supplies  a 
constant  current,  there  must  be  a  change  in  the  terminal  volt- 
age of  the  machine  with  a  change  in  load.  Thus,  if  there  are 
ten  arc  lamps  connected  in  series  and  there  is  a  drop  of  90 
volts  over  each  lamp,  the  terminal  voltage  of  the  machine 
must  be  (10X90)  or  900  volts,  neglecting  the  drop  in  the  line 
wires.  If  five  of  these  lamps  be  disconnected  from  the  line, 
the  circuit  still  being  closed,  the  voltage  required  at  the  ter- 
minals of  the  machine  will  be  (5X90)  or  450  volts.  The  cur- 
rent in  the  circuit  is  the  same  in  each  case.  The  output  of 
the  machine  in  the  second  case  then  would  be  only  one-half 
what  it  was  when  the  ten  lamps  were  in  operation  as  the 


DISTRIBUTION  AND  OPERATION 


259 


Fig.  215 


voltage  has  been  reduced  one-half,  the  current  remaining 
constant. 

293.      Series-Parallel    System    of    Distribution. — The    series- 
parallel  system  of  distribution  is  a  combination  of  the  series 
and   parallel   systems.     A   number  of  similar  lamps   may  be 
connected  in  series  and  the 
combination  then  connected 
to     the     supply     leads,     as 
shown  in  Fig.  215. 

The  same  current  exists 
in  each  lamp  of  a  given  set 
and  the  drop  in  potential 
over  the  various  lamps  that 
may  be  connected  in  series 
will  be  proportional  to  their 

respective  resistances.  This  system  is  usually  used  where 
it  is  desired  to  operate  a  number  of  lamps  or  motors  from  a 
line  whose  voltage  is  several  times  that  required  to  operate 
a  single  lamp  or  motor.  A  good  example  of  such  an  arrange- 
ment is  the  wiring  in  a  street  car  where  five  similar  110-volt 

lamps  are  connected  in  se- 
LI  ries  and  the  group  then  con- 

nected to  the  550-volt  source 
of  supply,  as  shown  in  Fig. 
215.  If  one  of  the  lamps  in 
any  group  should  burn  out 
or  for  some  reason  be  re- 
moved from  its  socket,  thus 
opening  up  the  circuit,  the 
remaining  lamps  of  that 
group  would  also  be  ex- 
tinguished. 

294.     Edison    Three -Wire 
System      of      Distribution. — 

Two  110-volt  generators,  (G1)  and  (Go),  are  shown  connected  in 
series  and  supplying  current  to  a  number  of  groups  of  incan- 
descent lamps,  Fig.  216.  Each  group  of  lamps  consists  of  two  110- 
volt  lamps  connected  in  series.  If  the  two  lamps  of  any  group 
have  the  same  resistance  there  will  be  the  same  drop  in 
potential  over  each,  since  they  both  carry  the  same  current, 
the  drop  being  equal  to  the  product  of  the  resistance  between 


Fig.  216 


260 


PEACTICAL  APPLIED  ELECTRICITY 


L, 


the  points  considered  and  the  current  in  the  resistance.  All 
of  the  points  numbered  (1),  (2),  (3),  etc.,  will  be  at  the 
same  potential,  since  the  drop  over  each  of  the  upper 
lamps  is  the  same  and  equal  to  the  drop  over  each  of  the 
lower  lamps.  If  these  various  points  be  connected  by  a  con- 
ductor there  will  be  no  change  in  the  division  of  the  current 

through  the  various 
branches  or  lamps.  The 
conductor  connecting  the 
points  (1),  (2),  and  (3) 
may  be  extended  back  and 
connected  between  the  two 
generators,  as  shown  in 
Fig.  217,  provided  the  ter- 
minal voltage  of  the  gen- 
erators is  the  same,  the 
point  (A)  between  them 
La  will  be  at  the  same  poten- 

Fis-  217  tial  as  the  points  (1),  (2), 

and  (3),  and  connecting  all  of  these  various  points  together 
by  the  lead  (N),  which  is  called  the  neutral  wire,  will  pro- 
duce no  change  in  the  division  of  the  line  current  through  the 
various  branches  of  the  load.  Such  an  arrangement  as  that 
shown  in  Fig.  217,  is  called  the  Edison  three-wire  system  of 
distribution. 

There  will  be  no  current  in  the  neutral  wire  when  the 
number  of  lamps  in  the  upper  set  is  the  same  as  the  number 
of  lamps  in  the  lower  set  and  the  current  in  the  leads  (L^) 
and  (L2)  will  be  the  same  in  value  and  in  the  direction  indi- 
cated oy  the  arrows  in  the  figure.  If  the  number  of  lamps 
in  the  lower  group  be  less  than  the  number  in  the  upper 
group,  there  will,  as  a  result,  be  a  current  in  the  neutral  lead 
and  the  direction  of  this  current  will  be  toward  the  gen- 
erators, or  toward  the  left,  when  the  polarity  of  the  machines 
is  the  same  as  that  shown  in  the  figure.  When  the  number 
of  lamps  in  the  upper  group  is  less  than  the  number  in  the 
lower  group,  the  current  in  the  neutral  lead  will  be  from  the 
generators  or  toward  the  right  when  the  polarity  of  the 
machines  is  the  same  as  that  indicated  in  the  figure.  The 
current  in  the  neutral  lead  will  always  be  equal  to  the  dif- 
ference in  the  value  of  the  current  in  the  two  outside  leads 


DISTRIBUTION  AND  OPEEATION 

(Li)  and  (L2)  and  its  direction  will  be  just  opposite  to  that 
of  the  current  in  the  outside  lead  that  is  greatest  in  value. 
When  there  is  no  current  in  the  neutral  lead,  the  load  is  said 
to  be  balanced  and  when  there  is  a  current  in  the  neutral 
lead  it  is  said  to  be  unbalanced. 

The  neutral  lead  in  no  case  will  carry  a  current  greater 
in  value  than  either  of  the  outside  leads  and,  as  a  result,  it 
need  not  be  greater  in  cross-sectional  area  than  the  outside 
leads.  Each  outside  wire  in  the  Edison  three-wire  system 
need  be  only  one-fourth  as  large  in  cross-sectional  area  to 
supply  the  same  number  of  lamps  with  the  same  per  cent 
voltage  drop  as  would  be  required  in  the  simple  110-volt 
system.  Only  one-fourth  as  much  copper  would  be  required 
in  the  three-wire  system  as  would  be  required  in  the  110-volt 
system  if  no  neutral  lead  was  used,  or  each  outside  lead 
would  represent  one-eighth 

of    the    total    copper    re-  +  75  L 

quired  in  the  110-volt  sys-        - -x- 
tem.     Since     the     neutral  ' 

lead  is  usually  made  equal 
in  area  to  the  outside 
leads,  there  will  be  three 
leads,  each  representing  in 
weight  one-eighth  of  the 
copper  required  for  the 
110-volt  system,  or  the  to- 
tal copper  required  for  the  p.g  21g 
three-wire  system  is  three- 
eighths  of  that  required  for  the  110-volt  system. 

If  no  neutral  lead  were  used,  it  would  be  impossible  to 
operate  one  lamp  alone  since  there  are  two  in  series;  but 
with  the  neutral  lead,  the  number  of  lamps  that  may  be  turned 
on  or  off  in  either  the  upper  or  the  lower  groups  is  entirely 
independent  of  the  number  of  lamps  turned  on  in  the  other 
group. 

295.  Drop  in  Potential  in  the  Neutral  Wire. — If  the  current 
taken  by  the  upper  group  of  lamps  in  Fig.  217  be  75  amperes 
and  the  current  taken  by  the  lower  group  be  50  amperes, 
there  will  be  a  current  of  25  amperes  in  the  neutral  lead  and 
the  direction  of  these  currents  will  be  that  shown  by  the 
arrows  in  Fig.  218.  Since  the  current  in  the  neutral  lead  is 


262  PBACTICAL  APPLIED  ELECTEICITY 

toward  the  generators,  the  end  connected  to  the  load  must  be 
at  a  higher  potential  than  the  end  connected  to  the  gen- 
erators. The  load  end  of  the  upper  lead  (Lj)  is  at  a  lower 
potential  than  the  generator  end  and  the  load  end  of  the 
lower  lead  (L2)  is  at  a  higher  potential  than  the  generator 
end.  The  drop  in  potential  in  these  various  leads  is  repre- 
sented by  the  dotted  lines  in  Fig.  218,  the  potential  falling 
off  along  each  lead  in  the  direction  of  the  current.  Assuming 
the  voltage  of  each  of  the  generators  is  112  volts  and  that 
this  voltage  remains  constant  regardless  of  the  load,  then  the 
voltage  over  the  upper  group  of  lamps  will  be  equal  to  112 
minus  the  algebraic  sum  of  the  drops  in  the  upper  lead  (L^) 
and  the  neutral;  while  the  voltage  over  the  lower  group  of 
lamps  will  be  equal  to  112  minus  the  algebraic  sum  of  the 
drop  in  the  lower  lead  (L2)  and  the  drop  in  the  neutral.  The 
drop  in  the  neutral  causes  a  decrease  in  the  voltage  over  the 
upper  group  of  lamps  and  it  tends  to  increase  the  voltage  over 
the  lower  group  of  lamps.  The  voltage  over  the  smaller  load 
will  be  greater  than  the  terminal  voltage  of  the  machine  con- 
nected to  that  load  when  the  current  in  the  neutral  is  greater 
than  the  current  in  the  ouside  lead  connected  to  the  smaller 
load,  if  the  neutral  and  outside  leads  have  the  same  resistance. 
If  a  three-wire  system  be  unbalanced  and  the  fuse  in  the 
neutral  lead  should  blow  or  the  neutral  should  be  opened,  the 
outside  leads  remaining  connected  to  the  generators,  there  will 
be  a  redistribution  of  the  total  voltage,  between  the  two  leads 
(Li)  and  (L2),  over  the  upper  and  lower  groups  of  lamps.  The 
drops  over  the  two  groups  would  bear  the  same  relation  to 
each  other  as  exists  between  the  resistances  of  the  two 
groups,  that  is,  the  group  containing  the  smaller  number  of 
lamps  or  having  the  larger  resistance  will  have  the  larger 
drop  over  it.  For  example,  if  there  be  ten  220-ohm  lamps 
connected  in  parallel  and  forming  one  group  and  only  one  220- 
ohm  lamp  in  the  other  group,  the  resistances  of  the  two 
groups  would  be  in  the  ratio  of  22  to  220.  This  would  result 
in  the  voltage  over  the  single  lamp  being  equal  to  229242  °* 
the  total  voltage  between  the  outside  leads  when  the  neutral 
lead  was  open.  If  the  total  voltage  between  the  outside  leads 
is,  say  220  volts,  then  the  voltage  over  the  single  lamp  will  be 
200  volts.  This  voltage  is  in  excess  of  the  value  the  lamp  will 
stand  and,  as  a  result,  the  lamp  filament  will  be  destroyed. 


DISTRIBUTION  AND  OPERATION 


263 


296.  Three-Wire  Generators.— In  the  operation  of  the 
Edison  three-wire  system  as  described  in  sections  (294)  and 
(295),  two  generators  are  required,  giving  rise  to  an  addi- 
tional expense  for  machines  as  compared  to  the  system  using 
a  single  generator;  and  on  this  account  a  special  type  of 
machine  has  been  devised  which  is  known  as  a  three-wire 
generator. 

The  total  voltage  of  any  direct- 
current  generator  can  be  divided 
into  two  parts  by  placing  a  brush 
midway  between  the  negative  and 
the  positive  brushes  of  the  ma- 
chine. The  coils  short-circuited 
by  this  additional  brush  would  be 
in  a  strong  magnetic  field  in  th6 
ordinary  machine  and,  as  a  result, 
there  would  be  considerable 
trouble  encountered  in  properly 

commutating  the  current.  This  additional  brush,  however,  can 
be  connected  to  a  coil  that  is  located  in  a  weak  magnetic  field 
and  the  commutation  greatly  improved  by  the  arrangement 
shown  in  Fig.  219,  which  consists  of  a  four-pole  field-magnet 
frame  wound  for  a  bipolar  machine,  there  being  two  adjacent 
north  poles  and  two  adjacent  south  poles.  The  brushes  (BA) 


Fig,  219 


Fig.  220 


and  (B2)  represent  the  main  brushes  of  the  machine  and  the 
brush  (B.T)  is  the  one  to  which  the  neutral  lead  is  connected. 
The  brush  (B;5)  is  negative  with  respect  to  the  brush  (Bj) 
and  positive  with  respect  to  the  brush  (B2).  The  magnetic 


264 


PKACTICAL  APPLIED  ELECTKICITY 


flux  from  the  two  north  poles  or  into  the  two  south  poles  is 
not  equal  on  account  of  armature  reaction  which  crowds  the 
flux  into  the  forward  pole.  This  results  in  the  voltage  between 
the  neutral  brush  and  one  main  brush  being  greater  in  value 
than  the  voltage  between  the  neutral  brush  and  the  other 
main  brush. 

Another   form  of   three-wire   generator   is   shown   diagram- 
matically  in  Fig.  220.     The  armature  winding  is  divided  into 


Fig.  221 

the  same  number  of  parts  as  there  are  magnetic  poles  on  the 
machine.  The  alternate  division  points  of  the  armature 
winding  are  connected  to  one  slip  ring  and  the  remaining 
division  points  to  a  second  slip  ring.  A  coil  of  low  resistance 
and  high  inductance,  called  a  reactor,  is  connected  to  two 
brushes  that  make  continuous  contact  with  the  two  slip  rings, 
and  a  tap,  which  is  taken  off  from  the  center  of  this  coil, 
forms  the  neutral  connection. 


DISTRIBUTION  AND  OPEKATION  265 

The  number  of  slip  rings  may  be  reduced  to  one  by  placing 
the  reactor  inside  of  the  armature  and  allowing  it  to  revolve 
with  the  armature,  the  middle  point  being  connected  to  the 
slip  ring.  Three-wire  generators  may  be  flat  or  over-com- 
pounded just  as  an  ordinary  generator  to  compensate  for 
armature  and  line  drops.  A  machine  manufactured  by  the 
General  Electric  Company  and  provided  with  two  slip  rings 
is  shown  in  Fig.  221. 

297.  Dynamotors. — The  dynamotor  is  a  machine  having 
one  magnetic  field  and  two  armature  windings.  It  is  a  com- 
bination of  generator  and  motor.  Each  of  the  armature  wind- 
ings is  usually  supplied  with  a  separate  commutator,  the 
electrical  connections  of  the  two  windings  being  independent. 
Either  of  these  windings  may  be  used  as  a  generator  or  a 
motor.  The  relation  of  the  terminal  voltage  of  the  generator 
side  and  the  impressed  voltage  on  the  motor  side  will  depend 
upon  the  relation  between  the  number  of  turns  in  the  two 
armature  windings.  If  the  number  of  inductors  in  the  winding 
of  the  generator  armature  winding  is  one-fourth  the  number 
of  inductors  in  the  motor  armature  winding,  then  the  voltage 
of  the  generator  will  be  practically  one-fourth  the  voltage 
impressed  upon  the  motor  armature.  The  current  output  of 
the  generator,  however,  will  be  practically  four  times  the  cur- 
rent taken  by  the  motor.  This  relation  of  current  and  volt- 
age in  the  generator  and  the  motor  armatures  results  in  there 
being  practically  the  same  number  of  ampere-turns  in  each 
armature  winding  when  the  machine  is  in  operation,  and  since 
the  current  in  the  generator  armature  winding  will  be  in  the 
opposite  direction  around  the  armature  core  to  what  it  is  in 
the  motor  armature  winding,  there  will  be  practically  no 
armature  reaction,  the  two  magnetizing  effects  neutralizing 
each  other. 

The  dynamotor  in  the  direct-current  circuit  corresponds  to 
the  transformer  in  the  alternating-current  circuit,  however,  it 
is  not  nearly  so  efficient  as  the  transformer. 

A  dynamotor  manufactured  by  the  Crocker  Wheeler  Com- 
pany is  shown  in  Fig.  222. 

298.  Dynamotor  as  an  Equalizer. — The  dynamotor  is  often 
used  to. equalize  the  difference  in  potential  between  the  out- 
side leads  in  a  three-wire  system  when  one  side  of  the  system 
is  carrying  a  larger  load  than  the  other.  When  the  dyna- 


266  PRACTICAL  APPLIED  ELECTRICITY 

mometer  is  thus  used,  it  is  called  an  equalizer;  the  wind- 
ings on  the  armatures  are  the  same  and  the  machine  can 
be  connected  to  the  line  as  shown  in  Fig.  223.  When  the 
two  sides  of  the  system  are  balanced  there  will  be  no 
current  in  the  neutral  lead  (N)  and  a  small  current  will 
pass  through  the  two  armature  windings  of  the  dyna- 
motor  in  series,  both  armatures  acting  as  motors.  If  one  side 


Fig.  222 

of  the  system  is  carrying  a  larger  load  than  the  other,  there 
will  be  a  greater  drop  in  the  leads  connected  to  it  and,  as  a 
result,  a  lower  voltage  will  exist  over  the  larger  load  than 
exists  over  the  smaller  load.  The  armature  winding  of  the 
balancer  connected  to  the  higher  voltage  will  act  as  a  motor 
and  drive  the  other  armature  winding  which  will  act  as  a 
generator,  and  the  pressure  of  this  generator  will  tend  to 
raise  the  voltage  of  the  more  heavily  loaded  side.  When  one 
of  the  windings  changes  from  a  motor  to  a  generator,  the 
current  in  it  reverses  in  direction.  The  direction  of  the 
currents  in  an  unbalanced  three-wire  system  that  is  being 
supplied  with  energy  from  a  main  generator  (G)  is  shown  in 
Fig.  223.  The  upper  commutator  of  the  balancer  is  connected 
to  the  generator  winding  of  the  dynamotor  and  is  supplying 
current  to  the  upper  or  larger  load,  and  the  lower  commutator 
is  connected  to  the  motor  winding  of  the  dynamotor  and  is 
taking  current  from  the  lightly  loaded  side. 


DISTKIBUTION  AND  OPERATION 


267 


299.  Motor-Generators,  or  Balancers. — A  motor-generator  in 
its  simplest  form  consists  of  a  motor  mechanically  connected 
to  a  generator.  The  number  of  generators  connected  to  any 
motor  is  not  limited  to  a  single  machine,  but  it  may  be  any 
number.  Thus,  a  motor  may 

be  electrically  connected  to  ^ 

a  source  of  energy  and  be 
operated  as  any  ordinary 
motor,  its  output  being  con- 
sumed in  driving  a  number 
of  generators  of  the  same  or 
unequal  voltages.  These  va- 
rious generators  can  in  turn  Fig.  223 
be  connected  and  supply  en- 
ergy to  a  multi-voltage  system,  as  shown  in  Fig.  224. 

A  motor-generator  is  quite  often  used  in  connection  with  a 
three-wire  system,  the  motor  and  the  generator  being  similar 
machines  and  rigidly  connected  together.  The  combination, 
when  so  used,  is  called  a  balancer  and  its  operation  is  prac- 
tically the  same  as  the  dyuamotor  previously  described.  The 
connection  of  a  balancer  composed 
of  two  simple  shunt  generators  to  a 
three-wire  system  is  shown  in  Fig. 
225.  The  two  machines  composing 
the  balancer  have  their  field  con- 
nections interchanged,  that  is,  the 
field  of  one  machine  is  connected 
to  the  terminals  of  the  other.  With 
this  arrangement  of  connections, 
the  voltage  regulation  is  greatly  im- 
proved, and  is  further  improved  by 
compounding  the  two  machines 
forming  the  balancer  and  connect- 
ing them  as  shown  in  Fig.  226. 

300.     Boosters. — When    electrical 
energy  is  being  distributed  from  a 

central  station  over  long  leads,  there  is  a  drop  in  volt- 
age due  to  the  resistance  of  the  leads  and,  as  a  result,  the 
voltage  at  the  receiving  end  of  the  line  is  less  than  it  is  at  the 
transmitting  end.  This  loss  in  voltage  can  be  compensated 
for  by  connecting  in  series  with  the  line  a  machine  called  a 


Pig.  224 


268 


PKACTICAL  APPLIED  ELECTKiCITY 


Fig.  225 


booster,  whose  action  in  the  circuit  is  to  produce  an  elec- 
trical pressure  which  acts  in  series  with  the  main  gen- 
erator pressure.  When  the  electrical  pressure  of  the 
booster  acts  in  opposition  to  the  voltage  of  the  main 
generator,  it  is  called  a  negative  booster.  The  booster 
may  be  driven  by  a  motor  connected  to  the  same  line 
the  booster  is  connected  to,  or  to  any  other  line,  or  it 

may  be  engine  -driven. 
There  are  a  number  of  dif- 
ferent forms  of  boosters 
but  only  two  will  be  men- 
tioned hare,  the  series  and 
the  shunt.  The  connection 
of  a  series  booster  in  a  line 
is  shown  in  Fig.  227.  The 
booster  (B)  is  driven  by  a 
compound  motor  (M)  con- 
nected as  shown  in  the  figure.  The  booster  itself  is  nothing 
more  than  a  series  generator  in  which  the  iron  of  the  mag- 
netic circuit  will  not  be  worked  above  the  knee  of  the  curve 
when  the  maximum  current  which  the  feeder  is  to  carry 
passes  through  the  series  winding  of  the  booster.  When  the 
magnetic  circuit  of  the  machine  is  worked  at  such  a  flux 
density,  the  relation  between  the  terminal  voltage  of  the 
machine  and  the  load  cur- 
rent la  practically  a  L, 
straight  line.  Now  by  prop- 
erly winding  the  machine, 
its  terminal  voltage  may 
be  made  to  increase  or  de- 
crease with  a  change  in 

current  in  the  feeder  just  ^ 

a  sufficient  amount  to  ex-  Fig.  226 

actly   compensate   for   the 

loss  in  voltage  due  to  copper  drop. 

In  charging  a  storage  battery,  the  voltage  of  the  line  from 
which  current  is  to  be  taken  in  charging  the  battery  may  in 
some  cases  be  less  than  is  required  to  give  the  battery  a  full 
charge.  In  such  a  case  a  small  shunt-wound  generator  (B) 
may  be  connected  in  series  with  the  battery,  as  shown  in  Fig. 
228.  The  voltage  of  this  generator  will  act  in  series  with  that 


DISTRIBUTION  AND  OPERATION 


269 


Fig.  227 


of  the  line  giving  a  resultant  voltage  sufficient  to  charge  the 
battery.  A  shunt  generator  when  so  used  is  called  a  shunt 
booster  and  it  may  be  either  motor-  or  engine-driven. 

301.  Operation    of    Generators    and    Motors    for    Combined 
Output. — The  load  generating  stations  are  called  upon  to  carry 
is,  as  a  rule,  not  constant 

in  value  throughout  the 
twenty-four  hours  of  the 
day.  If  one  large  generat- 
ing unit  were  installed  in 
a  station  supplying  a  vary- 
ing load,  the  efficiency  of 
the  plant  would  vary  be- 
tween very  wide  limits  on 
account  of  the  efficiency  of 

a  generator  varying  with  the  load  it  is  carrying.  A  generator 
is  usually  designed  so  that  it  will  have  the  maximum  efficiency 
at  its  rated  full  load,  it  decreasing  in  value  with  either  an  in- 
crease or  decrease  in  load.  Now  in  order  that  the  generating 
equipment  in  a  central  station  be  operated  at  its  maximum 
efficiency,  it  should  at  all  times  be  carrying  a  load  something 

near  its  full  capacity.     In 

4 ^       _r  L!          modern     central     stations 

this  is  accomplished  by 
using  a  number  of  genera- 
tors, instead  of  a  single 
machine,  their  combined 
capacity  being  sufficient  to 
carry  the  full  load  of  the 
station  and  so  arranged 
that  they  may  all  be  con- 
nected to  the  load  at  the  same  time.  The  number  of  genera- 
tors in  operation  may  be  changed  as  the  load  on  the  station 
changes  and  in  this  way  each  machine  will  operate  on  a  load 
corresponding  to,  or  near,  its  maximum  efficiency. 

For  a  similar  reason  to  that  mentioned  above,  motors  are 
connected  so  that  their  outputs  may  be  added,  the  number  of 
motors  in  operation  depending  upon  the  load. 

302.  Shunt  Generators  Connected  for  Combined  Output.— 
Two  simple  constant-voltage  shunt  generators   (Gi)  and  (G2) 
lire  shown  connected  in  parallel,  in  Fig.  229,  to  two  heavy 


Storage 
Battery 


Fig-.  228 


270 


PRACTICAL  APPLIED  ELECTRICITY 


Fig.  229 


leads  (LJ)  and  (L2)  called  bus-bars.    The  regulating  rheostats 
(Rj)  and  (R2)  in  the  field  circuits  should  be  adjusted  so  that 
the  total  load  connected  to  the  bus-bars  is  properly  divided 
between  the  two  generators.    If  the  voltage  regulation  of  the 
two  machines  is  not  maintained,  no 
serious    damage    will    result    except 
one  machine  will  not  carry  its  por- 
tion   of    the    load,    the    machine    of 
higher  voltage  carrying  the  greater 
portion  of  the  load.     The  voltage  of 
one   machine   may   drop   to    such   a 
value  that  it  will  change  to  a  motor 
but  still  no  serious  damage  will  re- 
sult as  the  shunt  motor  rotates  in 
the  same  direction  as  a  shunt  gen- 
erator, the   connections  of  the  field  windings  and  armature 
leads  remaining  unchanged. 

Two  or  more  shunt  generators  may  be  operated  in  series, 
as  shown  in  Fig.  224,  and  supply  energy  to  a  multi-voltage 
system  or  they  may  supply  energy  to  a  single  voltage  system, 
they  being  connected  in  series  so  as  to  increase  the  total 
voltage  between  the  leads. 

303.  Series  Generators  Con- 
nected for  Combined  Output. — Two 
series  generators  (Gi)  and  (G2) 
are  shown  connected  in  parallel  to 
the  bus-bars  (Lj)  and  (L2),  Fig-. 
230.  The  two  machines  will  oper- 
ate satisfactorily  in  parallel  so 
long  as  their  voltages  remain  the 
same.  If,  however,  the  voltage  of 
one  machine  falls  a  small  amount 

due  to  any  cause,  such  as  a  decrease  in  speed  of  its  prime 
mover,  there  will  be  a  decrease  in  current  supplied  by  it  and, 
as  a  result,  a  decrease  in  its  field  excitation,  which  results  in 
a  further  decrease  in  its  voltage.  This  unbalanced  condition 
continues  to  grow  until  the  lower  voltage  machine  is  con- 
verted into  a  motor,  and  since  the  direction  of  rotation  of  a 
series  generator  is  opposite  to  what  it  is  when  used  as  a 
motor,  the  results  may  be  very  serious  to  one  or  both  ma- 
chines. 


Fig.   230 


DISTRIBUTION  AND  OPEEATION 


271 


Fig.  231 


The  above  difficulty  in  operating  two  series-wound  gen- 
erators in  parallel  can  be  overcome  to  a  certain  extent  by 
allowing  the  armature  current  of  one  machine  to  pass  through 
the  field  of  the  other.  With  this  arrangement,  a  decrease  in 
armature  current  of  one  machine  causes  a  decrease  in  voltage 
of  the  other  machine  and,  as  a  result, 
the  first  machine  must  carry  its  proper 
share  of  the  load. 

The  current  in  the  various  field 
windings  may  be  made  independent  of 
the  voltage  of  the  different  machines 
by  connecting  the  junctions  of  the 
series  windings  and  brushes  by  a  low 
resistance  lead,  called  an  equalizer,  as 
shown  in  Fig.  231.  The  polarity  of 
the  points  connected  by  the  equalizer 
should  all  be  the  same.  When  this  connection  is  made,  the 
current  in  the  various  series  windings  is  practicplly  the  same 
provided  they  have  the  same  resistance.  It  is  impractical  to 
operate  series  generators  in  parallel  and,  as  a  result,  ,it  is 
never  done. 

Series  generators  are  operated  in  series  in  practice  in 
direct-current,  high  voltage  power  transmission.  The  gen- 
erators and  their  fields  are 
all  connected  in  series. 
Such  systems  are  used  in 
Europe  and  in  the  major- 
ity of  cases  they  are  con- 
stant-current systems,  the 
current  being  maintained 
constant  in  value  by  spe- 
cial regulating  devices 
which  change  both  the 
speed  of  the  prime  movers 
and  the  position  of  the 
brushes. 

304.  Compound  Generators  in  Parallel. — Compound  gen- 
erators may  be  operated  in  parallel  very  satisfactorily,  the 
connections  being  made  as  shown  in  Fig.  232.  It  is  not 
necessary  that  the  capacity  of  the  machines  connected  in 
parallel  be  the  same  but  they  must  have  the  same  terminal 


L, 


Shunt 
^^-TftftTvfir^ — ' 

Fig.  232 


£72  PRACTICAL  APPLIED  ELECTRICITY 

voltage  at  all  loads  and  the  resistance  of  their  series  fields 
must  be  to  each  other  inversely  as  their  capacities  for  the 
same  degree  of  compounding  in  order  that  the  total  load  he 
divided  in  proportion  to  their  respective  capacities  as  the  load 
changes  in  value.  When  it  is  desired  to  operate  two  machines 
having  different  degrees  of  compounding,  the  series  field  of 
the  machine  of  higher  compounding  should  be  shunted  with 
a  resistance,  or  sufficient  turns  in  the  series  windings  discon< 
nected,  so  that  its  compounding  will  correspond  to  that  of 
the  machine  with  which  it  is  to  operate.  A  resistance  may 
be  connected  in  parallel  with  the  series  winding  of  one  of  the 
machines,  if  the  currents  in  the  series  windings  are  not  in- 
versely as  the  capacities  of  the  two  machines. 

305.  Operation  of  Shunt  Motors  in  Series  and  Parallel. — 
Any  number  of  shunt  motors   will  operate   satisfactorily  in 
parallel  across  a  constant  pressure,  and  each  motor  may  be 
connected  to  a  separate  load  or  to  the  same  load. 

When  a  number  of  shunt  motors  are  operated  in  series 
across  a  constant-pressure  line,  they  must  be  rigidly  connected 
together.  If  they  were  not  rigidly  connected  together  and  the 
load  was  removed  from  one  of  the  motors,  it  would  race  and 
rob  the  remaining  motors  of  their  proper  share  of  the  total 
voltage.  It  is  not  practical  for  this  reason  to  operate  shunt 
motors  in  series  unless  they  be  rigidly  connected  together. 

306.  Operation  of  Series  Motors  in  Series  and   Parallel. — 
Any  number  of  series  motors  may  be  operated  in  series  on 
constant-current  circuits  and  their  operation  is  independent 
of  the  load  any  of  the  motors  may  be  carrying.     Any  motor 
may  be  overloaded  until  it  stops  without  interfering  with  the 
other  motors  connected  to  the  same  line,  since  the  current  in 
the  circuit  remains  constant  in  value  at  all  times.     Series 
motors  will  operate  satisfactorily  in  series  on  constant-voltage 
circuits   provided   they   are   rigidly   connected   together.     An 
example  is  to  be  found  in  starting  a  street  car  when  the 
motors   are   connected   in   series   groups   of   two   each.     The 
speed  of  each  motor  is  the  same  in  this  case,  provided  none 
of  the  wheels  slip,  and  the  voltage  over  each  will  be  prac- 
tically the  same.    If,  however,  the  wheels  to  which  one  of  the 
motors  is  geared  slip,  this  motor  will  speed  up  and  rob  the 
other  motor  of  its  proper  share  of  the  line  voltage  and,  as  a 


DISTRIBUTION  AND  OPERATION  £73 

result,  the  motor  having  the  lower  voltage  impressed  upon  it 
will  have  its  starting  torque  lowered. 

Any  number  of  series  motors  may  be  operated  in  parallel 
from  a  constant-voltage  line  provided  their  loads  are  not  dis- 
connected, which  would  result  in  the  motor  racing  and  no 
doubt  destroying  itself. 

307.  Operation    of   Compound    Motors. — Compound   motors 
are  operated  from  constant-voltage  lines  in  every  case  and 
each  has  its  own  load.    The  speed  regulation  of  the  compound- 
wound  motor,  when  the  series-  and  shunt-field  windings  are 
differentially    connected,   is   better   than   any   other   type   of 
direct-current  motor. 

308.  Switchboard. — A  switchboard  is  a  board,  of  insulating 
material  usually,  upon  which  the  indicating  instruments  and 
the  switches  used  in  connecting  various  electrical  circuits  are 
located.     It  is   customary   to   divide   a   switchboard  up   into 
sections  called  panels.    If  a  switchboard  be  used  in  connect- 
ing a  number  of  machines  to  a  certain  load,  it  will  be  divided 
into  what  are  called  generator  panels  and  feeder  panels.    All 
of  the  switches  and  instruments  associated  with  each  genera- 
tor being  mounted  on  the  generator  panels,  and  the  instru- 
ments and  switches  associated  with  the  feeder  circuits  being 
mounted  on   the  feeder  panels.     The   equipment  most   com- 
monly found  on  a  direct-current  switchboard  consists  of  volt- 
meters,    ammeters,     wattmeters,     ground     detectors,     circuit 
breakers,  fuses,  rheostats,   and   switches.     All  of  the  above 
equipment  has  been  described  with  the  exception  of  circuit 
breakers,  rheostats,  ground  detectors,  and  switches.     These 
devices  will  be  discussed  in  the  following  sections. 

309.  Circuit  Breakers. — A  circuit  breaker  is  a  switch  that 
may  be  closed  against  the  action  of  gravity  or  a  spring  and 
held  in  the  closed  position  by  means  of  a  suitable  latch,  which 
in  turn  is  controlled  by  one  or  more  solenoids.     A  solenoid 
may  be  connected   so  that  its   winding  will   carry  all  or  a 
definite  part  of  the  total  current  the  contacts  of  the  circuit 
breaker  carry  and  its  armature  may  be  so  adjusted  that  it. 
will  be  drawn  up  and  trip  the  latch  when  the  current  exceeds 
a  certain  value.     Such  a  circuit  breaker  is  called  an  over- 
load circuit  breaker. 

A  solenoid  may  be  so  constructed  that  it  will  trip  the  latch 


274 


PRACTICAL  APPLIED  ELECTRICITY 


of  the  circuit  breaker  when  the  current  in  the  circuit  is 
reversed.  Such  a  circuit  breaker  is  called  a  reverse-current 
circuit  breaker.  • 

A  circuit  breaker  in  which  the  latch  is  tripped  when  the 
current  falls  below  a  certain  value  is  called  an  under-load 
circuit  breaker. 

A  fourth  form  of  circuit  breaker  is  one  having  the  solenoid 
controlling  the  latch  connected  directly  across  the  line  and  so 
arranged  thaf  the  breaker  is  opened  automatically  when  the 
voltage  drops  below  a  certain  value.  This  form  of  circuit 
breaker  is  called  a  no-voltage  circuit  breaker.  Various  com- 
binations of  the  above  forms  of  circuit  breakers  may  be  made 
which  will  meet  practically  all  requirements.  An  over-load 
and  no-voltage  circuit  breaker  combined  is  shown  in  Fig.  233. 

310.  Rheostat. — A  rheostat  is  a 
resistance  whose  value  may  be 
varied.  There  are  numerous  forms 
of  rheostats,  their  construction  in  a 
measure  being  determined  by  the 
particular  use  to  which  they  are  to 
be  placed.  A  form  of  rheostat  used 
in  regulating  the  shunt-field  current 
of  generators  is  shown  in  Fig.  234. 
This  consists  of  a  number  of  small 
coils  of  wire  connected  in  series 
and  their  junctions  joined  to  a 
number  of  contact  buttons  over 
which  a  metal  arm  passes.  One 
terminal  of  the  rheostat  is  the  arm 
that  moves  over  the  contact  but- 
tons and  the  other  terminal  is  one 
of  the  end  coils.  The  variation  in 

current  that  may  be  produced  by  such  a  rheostat  will  depend 
upon  the  relation  between  the  resistance  of  the  circuit  in 
which  the  rheostat  is  connected  and  its  own  total  resistance. 
Such  rheostats,  as  a  rule,  have  rather  a  small  current- 
carrying  capacity. 

A  rheostat  composed  of  a  number  of  carbon  plates  mounted 
side  by  side  is  shown  in  Fig.  235.  The  resistance  of  this 
rheostat  is  changed  by  varying  the  pressure  between  the 
various  plates  of  carbon  between  the  end  plates,  by  means  of 


Fig.  233 


DISTRIBUTION  AND  OPEEATION 


275 


a  small  handle  shown  in  the  figure.     The  resistance  of  this 
rheostat  is,   as   a  rule,   rather  low,  but  its   current-carrying 
capacity  is  quite  large.    It 
operates  very  satisfactorily 
in  low  voltage  circuits  and 
the  variations  in  its  resist- 
ance   can    be    made    very 
gradual. 

Rheostats  are  usually 
controlled  from  the  switch- 
boards when  used  in  ad- 
justing the  field  current  of 
machines  and  the  control 
is  accomplished  by  a  small 
handle  on  the  face  of  the 
board,  the  rheostat  being 
usually  mounted  back  of 
the  board. 

311.  Ground   Detectors. — A  ground  detector  is   an  instru- 
ment used  in  measuring  the  insulation  resistance  between  any 
line  connected  to  the  switchboard  and  ground.    It  is  really  a 
special  form  of  series  voltmeter  marked  in  some  cases  to  read 
directly  in  ohms. 

312.  Switches. — Switches  are  devices  that  are  connected  in 


Fig.  234 


Fig.  235 

a  circuit  to  facilitate  its  being  closed  or  opened.  They  may  be 
single-pole,  double-pole,  etc.,  depending  upon  the  number  of 
circuits  that  are  interrupted  when  the  switch  is  opened.  A 
double-pole  double-throw  switch  is  shown  in  Fig.  236.  This 
switch  is  so  constructed  that  the  circuits  are  connected  to  it 
back  of  the  board  upon  which  it  is  mounted.  The  size  of  the 


276  PRACTICAL  APPLIED  ELECTRICITY 

jaws  and  blades  of  a  switch  will  depend  upon  the  value  of  the 
current  the  switch  is  designed  to  carry,  and  the  distance 
between  the  various  parts  that  are  connected  to  the  different 
leads  will  depend  upon  the  voltage. 

313.  Instructions  for  Starting  a  Generator  or  Motor. — In 
starting  a  machine  make  sure  the  commutator  is  perfectly 
clean.  Examine  the  brushes  carefully  to  see  that  they  are  all 
making  good  contact  with  the  commutator  and  that  they  are 
in  their  proper  position,  which  should  be  indicated  by  a  mark 
on  the  rocker  arm  supporting  them.  If  there  happens  to  be 
no  such  mark,  their  position  must  be  adjusted  after  the 
machine  is  in  operation,  it  being  indicated  by  a  maximum 
voltage  in  the  case  of  a  generator  and  a  minimum  speed  in 


Fig.  236 

the  case  of  a  motor.  They  are,  however,  usually  advanced 
a  little  beyond  this  position  in  a  generator  and  back  of  it  in 
a  motor  in  order  to  reduce  the  tendency  for  sparking.  Exam- 
ine all  connections  and  see  that  all  screws  and  bolts  are  tight. 
Fill  the  oil  cups  and  see  that  they  are  supplying  oil  to  the 
parts  they  are  supposed  to  lubricate. 

If  the  machine  is  being  started  for  the  first  time,  make  sure 
that  it  turns  over  freely  and  that  the  armature  is  properly 
balanced  and  that  it  is  centrally  located  in  the  magnetic  field. 
After  it  has  been  thus  inspected,  the  machine  should  be 
started  up  and  its  speed  increased  gradually  when  possible, 
with  the  switches  all  left  open  in  the  case  of  a  generator. 
If  the  machine  is  being  started  for  the  first  time,  it  should 
be  run  for  a  number  of  hours  without  load  and  the  load  then 


DISTRIBUTION  AND  OPEKATION 


277 


Fig.  237 


278  PRACTICAL  APPLIED  ELECTRICITY 

gradually  applied,  the  attendant  being  in  readiness  at  all 
times  to  disconnect  or  stop  it  if  anything  should  go  wrong. 

314.  Starting  and  Stopping  Compound  Generators  that  are 
Operating  in  Parallel. — A  diagram  of  the  wiring  of  a  switch- 
board used  in  connecting  two  generators  in  parallel  and  to  a 
common  load  or  in  connecting  either  generator  to  a  separate 
load  is  shown  in  Fig.  237.  The  left-hand  panel  is  the  gen- 
erator panel  for,  say  generator  (Gi);  the  middle  panel  is  the 
generator  panel  for  generator  (G2) ;  and  the  right-hand  panel 
is  the  feeder  or  load  panel.  On  each  generator  panel  there  is 
mounted  a  wattmeter  (W),  a  circuit  breaker  (CB),  a  main 
generator  switch,  an  equalizer  switch,  a  field-regulating  rheo- 
stat (shown  in  the  figure  by  the  dotted  circles),  a  voltmeter, 
and  an  ammeter.  The  ammeter  shunt  is  shown  connected  in 
series  with  the  lead  from  the  generator  and  it  should  always 
be  connected  in  the  lead  that  goes  to  the  terminal  of  the 
generator  opposite  the  one  to  which  the  equalizer  lead  is 
connected.  If  it  were  connected  in  the  other  lead  it  would  not 
necessarily  indicate  the  current  that  really  exists  in  the  arma- 
ture of  the  generator  unless  there  was  no  current  in  the 
equalizer. 

The  following  apparatus  is  mounted  on  the  feeder  panel 
shown  in  Fig.  237.  Two  lines  (Li)  and  (L2)  are  connected 
to  the  central  points  of  the  double-pole  double-throw  switches 
(S3)  and  (S5),  one  lead  of  each  line  passing  through  the  cur- 
rent coils  of  the  two  wattmeters  (W3)  and  (W4).  The  outside 
points  of  the  switches  (S3)  and  (S5)  are  connected  to  the 
bus-bars  of  the  two  generators  (Gi)  and  (G2).  The  upper  and 
the  lower  contacts  of  the  switch  (S4)  are  connected  to  the  bus- 
bars of  the  two  generators  and  when  this  switch  is  closed  the 
two  machines  will  be  connected  in  parallel,  provided  the 
terminals  of  the  switch  (S4)  that  are  connected  when  the 
switch  is  closed  are  of  the  same  polarity.  A  voltmeter  (Vc) 
is  mounted  on  this  panel  and  its  terminals  are  connected  to 
the  central  points  of  the  small  double-pole  double-throw  switch 
(S8),  which  has  its  upper  and  lower  contacts  connected  to  the 
terminals  of  the  two  generators  (G±)  and  (G2). 

Assuming  now  one  machine  is  in  operation  and  connected 
to  one  or  both  of  the  loads  and  it  is  desired  to  connect  the 
idle  machine  in  parallel  with  the  one  already  in  operation. 
The  two  loads  can  be  connected  to  one  machine  by  closing  the 


DISTRIBUTION    AND    OPERATION  279 

switches  (S3),  (S4),  (S5),  and  the  proper  generator  switch. 
Bring  the  generator  up  to  speed,  close  the  equalizer  switches 
(S6)  and  (S7),  and  adjust  its  shunt-field  current  to  such  a 
value  that  its  terminal  voltage  is  a  little  in  excess  of  that 
between  the  bus-bar  to  which  the  machine  is  to  be  connected. 
This  can  be  determined  by  noting  the  indications  of  the  two 
voltmeters  (Vi)  and  (V2),  respectively,  or  the  voltmeter  (Vc) 
may  be  thrown  from  one  circuit  to  the  other,  by  operating  the 
switch  (S8)  and  its  indication  noted  when  it  is  connected  to 
the  two  circuits.  Using  a  single  voltmeter  eliminates  the 
possibility  of  an  error  due  to  the  two  separate  voltmeters 
not  indicating  the  same,  even  though  they  be  connected  to 
the  same  pressure.  When  the  voltage  of  the  incoming  ma- 
chine has  been  adjusted  to  the  proper  value,  the  main  switch 
may  be  closed  and  the  field  current  adjusted  to  such  a  value 
that  the  load  is  divided  between  the  two  machines  in  propor- 
tion to  their  capacities.  You  should  always  be  absolutely 
sure  that  the  points  of  the  last  switch  you  close  in  connecting 
the  machines  in  parallel  is  of  the  proper  polarity,  positive  to 
positive  and  negative  to  negative,  before  the  switch  is  closed. 
If  the  indications  of  the  voltmeters  depend  upon  the  direction 
of  the  current  in  their  windings,  and  you  are  sure  there  has 
been  no  change  in  the  connections  back  of  the  board  or  at  the 
machines,  you  can  then  close  the  paralleling  switch  when  all 
of  the  voltmeters  read  in  the  proper  direction. 

When  it  is  desired  to  disconnect  a  machine  from  the  line,  its 
voltage  is  lowered  by  reducing  its  shunt-field  current  and,  as 
a  result,  it  fails  to  carry  its  proper  share  of  the  load.  The 
main  generator  switch  should  be  opened  when  the  current 
output  of  the  generator  has  decreased  to  almost  zero  value. 
The  equalizer  switch  may  then  be  opened  and  the  machine 
shut  down. 


CHAPTER  XIV 

DISEASES  OF   DIRECT-CURRENT  DYNAMOS 

315.  Sparking  at  the  Brushes  Due  to  Fault  of  the 
Brushes. — 

(1)  Brushes  not  set  diametrically  opposite. 

(Rla)  Should  have  been  properly  set  at  first  while 
at  rest  by  counting  bars,  by  measurement,  or  by  use 
of  reference  marks  on  the  commutator. 

(Rib)  Can  be  done  if  necessary  while  running  by 
bringing  the  brushes  on  one  side  to  the  least 
sparking  point  by  moving  the  rocker  arm  and  then 
adjusting  the  brushes  on  the  other  side  to  the  least 
sparking  point  by  moving  the  rocker  arm  and  then 
brush  holder  and  then  clamping. 

(2)  Brushes  not  set  in  neutral  point. 

(R2a)  Move  the  rocker  arm  slowly  back  and  foith 
until  the  sparking  stops.  See  (R58e). 

(3)  Brushes  not  properly  trimmed. 

(R3a)  Brushes  should  be  always  kept  properly 
trimmed  and  set.  If  sparking  begins  from  this 
cause  and  dynamo  cannot  be  shut  down,  bend  back 
the  brushes  and  cut  off  loose  and  ragged  wires  if 
metal  brushes  are  used.  Retrim  as  soon  as  pos- 
sible after  run  is  over.  If  there  are  two  or  more 
brushes  in  each  set,  they  may  be  changed  one  at 
a  time  for  new  and  properly  trimmed  ones  during 
the  run  on  any  low  voltage  machine.  See  number 
(38).  To  trim,  clean  them  from  oil  or  dirt  with 
benzine,  soda,  or  potash,  then  file  or  grind  to  a 

Note. — The  list  of  dynamo  diseases  given  in  this  chapter 
was  taken  from  a  large  chart,  suitable  for  framing,  that  is 
published  by  the  Guarantee  Electric  Company,  Chicago. 

280 


DISEASES  OF  DIRECT-CURRENT  DYNAMOS        281 

standard  jig  and  reset  carefully  as  at  (Rla),  (Rib). 
See  (R38a)  and  (R38b). 

(4)  Brushes  not  in  line. 

(R4a)  Adjust  each  brush  of  a  given  set  until  they 
are  all  in  line  and  square  with  the  same  commu- 
tator bar,  bearing  evenly  for  their  entire  width, 
unless  purposely  staggered.  See  (R13a). 

(5)  Brushes  not  in  good  contact. 

(R5a)     Clean  the  commutator  of  all  dirt,  oil  or  grit, 

so  that  brushes  touch. 

(R5b)  Adjust  pressure  by  tension  screws  and 
springs  until  light,  firm,  yet  even  contact  is  made. 
Pressure  should  be  about  1.25  pounds  per  square 
inch.  See  number  (38). 

316.     Sparking   at   the   Brushes   Due  to    Fault  of   the   Com- 
mutator or  Magnetic  Field. — 

(6)  Commutator  rough,  worn  in  grooves  or  ridges. 

(7)  Commutator  not  round. 

(R6a  and  R7a)  Grind  down  the  commutator  with  fine 
sand  paper  (never  emery  in  any  form)  laid  in  stock 
curved  to  fit  the  commutator.  Polish  with  a  soft, 
clean  cloth. 

(R6a  and  R7b)  If  too  bad  to  grind  down,  turn  off  with 
a  special  tool  and  rest  while  turning  slowly  in  the 
bearings,  or  remove  the  armature  from  bearings 
and  turn  off  with  light  cuts  in  lathe. 

Note. — Armature  should  have  from  ifa"  to  %"  en(* 
motion  so  as  to  distribute  wear  evenly  and  prevent 
wearing  in  ruts  or  ridges.  Brushes  may  be  shifted 
sideways  occasionally  to  assist  in  distribution  of 
the  wear.  See  number  (31). 

(8)  One  or  more  high  commutator  bars. 

(R8a)  Set  the  high  bar  down  carefully  with  a  mal- 
let or  block  of  wood,  being  careful  not  to  bend, 
bruise  or  injure  the  bar  and  then  tighten  the 
clamping  rings.  If  this  does  not  remedy  the  fault, 
file,  grind  or  turn  the  high  bar  down  to  the  level  of 
the  other  bars.  The  high  bar  may  cause  the 
brushes  to  jump  or  vibrate  so  as  to  "sing."  See 
number  (38). 

(9)  One  or  more  low  commutator  bars. 


282  PRACTICAL  APPLIED  ELECTRICITY 

(R9a)  Grind  the  remainder  of  the  commutator  down 
to  a  true  surface  so  as  to  remove  low  spots. 

Note. — The  insulation  between  the  segments  may  be 
high,  due  to  its  not  wearing  as  fast  as  the  metal  of 
the  segments.  Insulation  should  be  turned  down  to 
level  of  segments  to  remedy  this  fault. 

(10)  Weak  magnetic  field. 

(A)  Broken  circuit  in  field. 

(RlOa)  Solder  or  repair  broken  connection.  Re- 
wind if  the  brake  is  inside  of  the  winding. 

(B)  Short-circuit  of  the  coils. 

(RlOb)     Repair   if  external   and   rewind   if  internal. 

(C)  Dynamo  not  properly  wound  or  without  proper 
amount  of  iron. 

(RIOc)     No  remedy  but  to  rebuild. 

317.     Sparking  at  the  Brushes  Caused  by  an  Excessive  Cur- 
rent in  the  Armature  Due  to  an  Overload. — 

(11)  Generator.   (A)     Too   many    lamps    on   the   circuit 

( constant-potential  system ) . 

(B)  Ground  and  leak  from  short-circuit 
on  the  line. 

(C)  Dead  short-circuit  on  the  line. 
Motor.         (D)     Excessive    voltage   on    a    constant- 
potential  circuit. 

(E)  Excessive  amperage  on  a  constant- 
current  circuit. 

(F)  Friction.     See  section  (321). 

(G)  Too    great   a   load   on    the    pulley. 
See  section  (321). 

(Rlla)  Reduce  the  number  of  lamps  and  thus  di- 
minish the  current  called  for. 

(Rllb)     Test  out,  locate  the  ground  and  repair. 

(Rile)  Dead  short-circuit  will  or  should  blow  the 
safety  fuse.  Shut  down  the  dynamo,  locate  and 
repair  the  fault.  Put  in  new  fuse  before  starting 
again.  Fuse  should  not  be  inserted  until  the  fault 
is  corrected,  as  it  will  blow  again  on  starting  up 
the  machine. 

(Rlld)  Use  the  proper  value  of  current  for  a  motor 
and  no  other. 


DISEASES  OF  DIRECT-CURRENT  DYNAMOS'        283 

(Rile)     Make  sure  you  have  the  proper  rheostat  or 

controlling  switch. 
(Rllf)     Reduce  the  load  to  the   proper  amount  for 

rating  of  the  motors. 
(Rllg)     Remedy   any   cause   of   trouble    from   undue 

friction.     See  section   (321). 

318.     Sparking   at  the   Brushes   Due  to   Fault  of  the   Arma- 
ture.— 

(12)  Short-circuited  coil  in  the  armature. 

(R12a)  Look  for  copper  dust,  solder,  or  other  cause 
for  metallic  contact  between  commutator  bars  and 
remove. 

(R12b)  See  that  the  clamping  rings  are  properly 
insulated  from  commutator  bars,  and  from  car- 
bonized oil  and  copper  dust  or  dirt  which  may  form 
a  short-circuit. 

(R12c)  Test  for  internal  short-circuit  or  cross-con- 
nection; if  found,  reinsulate  the  conductor,  change 
the  connection,  or  rewind  armature  to  correct. 

(R12d)  Examine  the  insulation  of  the  brush  holders 
for  the  fault.  Dirt,  oil,  or  copper  dust  may  form  a 
short-circuit  from  brush  holder  to  rocker  arm,  and 
thus  short-circuit  the  machine. 

(13)  Broken  circuit  in  the  armature. 

(R13a)  Bridge  the  break  temporarily  by  staggering 
the  brushes  till  the  run  is  finished,  then  test  out 
and  repair  the  fault.  This  is  only  a  temporary 
make-shift  to  try  to  stop  the  bar  sparking  during 
a  run  when  dynamo  cannot  be  shut  down. 

(R13b)  If  the  dynamo  can  be  shut  down,  look  for 
broken  or  loose  connection  to  the  bar  and  repair. 

(R13c)  If  the  coil  is  broken  inside,  rewinding  is  the 
only  sure  remedy.  The  break  may  be  bridged  tem- 
porarily by  hammering  the  disconnected  bar  until 
it  makes  contact  across  the  mica  to  the  next  bar 
of  the  commutator.  This  remedy  is  of  doubtful 
value  if  done.  The  bars  must  be  repaired  and 
insulation  replaced  again  after  fault  is  corrected. 

(R13d)  Solder  the  commutator  lugs  together  or 
bridge  across  them  with  piece  of  heavy  wire  and 
thus  cut  out  the  broken  coil.  Be  careful  not  to 


284  PRACTICAL  APPLIED  ELECTRICITY 

short-circuit  a  good  coil  in  soldering,  and  thus 
cause  sparking  from  a  short-circuited  coil,  as  in 
number  (12). 

(14)  Cross-connection  in  the  armature. 

(R14a)  Cross-connections  may  have  the  same  effect 
as  a  short-circuit  and  they  are  to  be  treated  as 
such.  See  number  (12).  Each  coil  should  show  a 
complete  circuit  with  no  connection  to  any  other 
coils. 

319.  Heating  of  the  Armature. — 

(15)  Overloaded   or  not   centrally   located  between  the 
poles. 

(16)  Short-circuit.    See   numbers    (11),    (12),    (13),   and 
(14). 

(17)  Broken  circuit. 

(18)  Cross-connection. 

(19)  Moisture  in  the  armature  coils. 

(R19a)  Dry  out  the  coils  by  slow  heat,  which  may 
be  done  by  sending  a  current  through  the  armature 
regulated  not  to  exceed  the  proper  value.  If  not  so 
bad  as  to  cause  a  short-circuit,  cross-connection,  or 
too  much  heat,  the  moisture  may  be  dried  out  by 
the  heat  of  its  own  current  while  running. 

(20)  Eddy  currents  in  the  armature  core. 

(R20a)  The  iron  of  the  core  may  be  hotter  than  the 
coils  after  a  short  run  due  to  a  faulty  armature 
core,  which  should  be  finely  laminated  and  the 
lamime  insulated.  No  remedy  but  to  rebuild. 

(21)  Friction. 

(R21a)  Hot  bars  and  journals  may  affect  the  tem- 
perature of  the  armature.  See  section  (321). 

320.  Heating  of  the  Field  Coils.— 

(22)  An  excessive  current  in  the  field  circuit. 

(R22a)  Shunt  machine.  Decrease  the  voltage  at  the 
terminals  by  reducing  the  speed,  or  increasing  the 
resistance  of  the  field  coils  by  winding  on  more 
wire,  or  rewind  them  with  finer  wire,  or  put  a 
resistance  in  sertes  with  the  field. 

(R22b)  Series  machine.  Shunt  a  portion  of  the 
current,  or  otherwise  decrease  the  current  in  the 
field  windings,  or  take  off  one  or  more  layers  of 


DISEASES  OF  DIRECT-CURRENT  DYNAMOS        285 

wire,  or  rewind  the  fields  with  a  coarser  wire. 
Note. — An  excessive  current  nay  be  due  to  a  short- 
circuit  or  from  moisture  in  the  coils  acting  as  a 
short-circuit.    See  number  (24). 

(23)  Eddy  currents  in  the  pole  pieces. 

(R23a)  The  pole  pieces  may  be  hotter  than  the  field 
coils  after  a  short  run  due  to  faulty  construction 
or  to  a  fluctuating  current  in  the  latter;  regulate 
and  steady  the  current. 

(24)  Moisture  in  the  field  coils. 

(R24a)     The  coils  show  a  resistance  lower  than  nor- 
mal, which   may  be   caused   by  a   short-circuit  or 
contact  with  the  iron  of  the  dynamo.     Dry  out  the 
coils  as  in  number  (19).     See  note  under   (R22b). 
321.     Heating  of  the  Bearings. — 

(25)  Not  enough  or  poor  quality  of  oil. 

(R25a)  Supply  plenty  of  good  clean  oil  and  see  that 
it  feeds  properly.  Oil  should  be  best  quality  min- 
eral oil,  filtered  clean  and  free  from  grit. 

Note. — Be  careful  not  to  flood  the  bearings  so  as  to 
force  oil  upon  the  commutator,  or  into  the  insula- 
tion of  the  brush  holders,  as  it  will  gradually  char 
and  gather  copper  dust  and  form  a  short-circuit. 
See  (R12b)  and  (R12d). 

(R25b)  Vaseline,  cylinder  oil,  or  other  heavy  lubri- 
cant may  be  used  if  ordinary  oil  fails  to  remedy 
the  hot  box.  Use  till  run  is  over,  then  clean  up 
and  adjust  the  bearings. 

(26)  Dirt,  grit,  or  other  foreign  matter  in  the  bearings. 
(R26a)     Wash  out  the  grit  by  flooding  the  bearings 

with  clean  oil  until  run  is  over.  Be  careful,  how- 
ever, about  flooding  the  commutator  or  brush 
holders.  See  note  under  (R25a). 

(R26b)  Remove  the  cap  and  clean  the  journals  and 
bearings,  then  replace  the  cap  and  lubricate  well. 

<R26c)  After  the  run  is  over  (or  if  shut-down  is 
made),  remove  the  bearings  completely,  cool  off 
naturally,  and  polish  everything  free  from  grit,  and 
set  up  again. 

(27)  Rough  journals  or  bearings. 

(R27a)     Smooth  and  polish  in  a  lathe,  removing  all 


286  PRACTICAL  APPLIED  ELECTRICITY 

cuts,  burs,  scratches,  and  tool  marks,  then  make 
new  bearings  (of  babbitt  or  other  metal)  to  prop- 
erly fit. 

(28)  Journals  too  tight  for  bearings. 

(R28a)  Slacken  the  bolts  in  the  cap,  put  in  packing 
pieces  till  run  is  over,  then  fit  to  smooth  bearing 
and  easy  rotation  by  hand  (if  the  machine  is 
small). 

(R28b)  Turn  down  smooth  and  repolish  the  journal, 
or  ream  or  scrape  the  bearings  until  they  fit  prop- 
erly. 

(29)  Bent  or  sprung  shaft. 

(R29a)  Bend  or  turn  the  shaft  true  by  caretul 
springing  or  turning  in  lathe. 

(30)  Bearings  out  of  line. 

(R30a)  Loosen  the  base  of  the  bearings  and  shift 
them  until  the  armature  turns  freely  by  hand  with 
belt  off  and  it  is  at  the  same  time  in  the  center  of 
the  polar  space.  Remount,  bolt,  and  dowel-pin 
holes,  and  fit  new  dowels  to  allow  new  position  to 
be  kept  when  bolts  are  drawn  up  tight.  If  shaft 
need  be  raised  or  lowered,  then  pack  up  or  trim 
down  the  foot  of  the  bearing  to  allow  the  proper 
setting. 

(31)  End   pressure  of  the  pulley  hub  or  shaft  collars 
against  the  bearings. 

(R31a)  See  that  the  foundation  ia  level  and  that  the 
armature  moves  freely  with  a  small  amount  of  end 
motion. 

(R31b)  If  there  is  no  end  motion,  then  turn  off  the 
shoulders  on  the  shaft  or  file  or  trim  off  the  ends 
of  the  bearings  until  the  necessary  end  motion  is 
obtained. 

(R31c)  Then  line  up  the  shaft,  pulley,  and  belt  so 
that  no  end  thrust  is  maintained  on  the  shaft,  but 
the  armature  has  free  end  play  while  in  motion. 

(32)  Too  great  a  load  or  strain  on  the  belt. 

(R32a)  Reduce  the  load  so  that  the  belt  may  be 
slackened  and  yet  not  slip.  Avoid  vertical  belts  if 
possible.  (Vibration  and  flapping  of  belt  causes 
lamps  to  flicker.) 


DISEASES  OF  DIEECT-CUKKENT  DYNAMOS        287 

(R32b)  Use  larger  pulleys,  wider  and  longer  belts. 
Run  with  slack  side  on  top  to  increase  the  adhesion 
and  pull  of  belt  without  excessive  tightening.  Belt 
should  be  tightened  just  enough  to  drive  the  full 
load  smoothly  without  vibration  or  flapping. 

(33)  Armature  being  not  centrally  located  between  the 
poles. 

(R33a)  Bearing  may  be  worn  out,  letting  the  arma- 
ture move  out  of  center  and  should  be  replaced. 
See  number  (30). 

(R33b)  Center  the  armature  in  the  polar  space  and 
adjust  the  bearings  to  the  new  position.  See 
number  (30). 

(R33c)  File  out  the  polar  space  to  give  an  equal 
clearance  all  around  the  armature. 

(R33d)  Spring  the  pole  away  from  the  armature 
and  secure  it  in  place.  This  will  be  a  difficult  if 
not  an  impossible  job  in  large  and  rigid  machines. 
322.  Noise.— 

(34)  The  armature  or  pulley  out  of  balance. 

(R34a)  The  armature  and  pulley  should  have  been 
properly  balanced  when  made.  Their  construction 
may,  however,  be  somewhat  improved  by  mounting 
them  on  knife  edges  and  adding  weight  to  the  light 
side  until  balanced. 

(35)  The    armature    strikes    or    rubs    against   the    pole 
pieces. 

(R35a)  Bend  or  press  down  and  secure  any  project- 
ing wires.  Secure  rigidly  with  proper  tie  bands  of 
strong  wire. 

(R35b)  File  out  the  pole  pieces  where  armature 
strikes.  See  numbers  (30)  and  (33)  for  possible 
remedies. 

(36)  The  collars  or  shoulders  on  the  shaft,  hub,  or  web 
of  pulley  strike  or  rattle  against  the  bearing. 

(R36a)  The  bearing  may  be  worn  out  and  too  loose 
and  therefore  rattle,  new  bearing  needed.  See 
numbers  (30)  and  (33). 

(37)  Loose  screws,  bolts,  or  connections. 

(R37a)  Tighten  up  all  the  screws,  bolts,  and  connec- 
tions to  firm  bearing  and  keep  them  so  by  daily 


2SS  PRACTICAL  APPLIED  ELECTRICITY 

attention.  The  jar  and  movement  of  dynamos 
tends  to  work  screwed  connections  loose  when  not 
held  by  check  nuts. 

(38)  Singing  or  hissing  of  the  brushes.     See  numbers 
(3),  (4),  and  (5). 

(R38a)  Apply  a  little  mineral  oil  or  better  yet  vase- 
line or  hold  a  piece  of  stearic  acid  (adamantine) 
candle  to  the  commutator  and  then  wipe  off.  Just 
a  faint  trace  of  oil  or  grease  is  all  that  is  needed. 

(R38b)  Lengthen  or  shorten  the  brushes  in  the 
holder  until  firm  yet  gentle  pressure  is  maintained 
free  from  any  hum  or  vibration.  See  numbers  (3), 
(6),  (7),  (8),  (9),  and  (31). 

(39)  Flapping  or  pounding  of  the  belts,  joints,  or  lacing. 
(R39a)     Use  an  endless  belt.    If  a  laced  belt  must  be 

used,  have  square  joints  properly  laced. 

(40)  Slipping  of  the  belt  due  to  an  overload. 

(R40a)  Tighten  the  belt  or  reduce  the  load.  See 
number  (32). 

(41)  Humming  of  the  armature  lugs  or  teeth  as   they 
pass  the  pole  pieces. 

(R41a)  Slope  the  ends  of  the  pole  pieces  so  that 
the  armature  teeth-  do  not  pass  the  edges  all  at 
once. 

(R41b)     Decrease    the    magnetism    of    the    fields    or 

increase  the  magnetic  capacity  of  the  teeth. 
323.     Speed  Too  High. — 

(42)  The  engine  fails  to  regulate  under  a  varying  load. 
(R42a)     Adjust  the   governor  to   the  ^proper  regula- 
tion if  possible;    if  not,  get  a  better  engine.     The 
engine  should  regulate  closely  from   "no  load"   to 
"full  load"  with  the  proper  steam  supply. 

(43)  Series  motor  takes  too  much  current  for  a  given 
load  and  the  motor  runs  away.     (Load  on  the  series 
motor  is  too  small.) 

(A)  Series  motor  on  a  constant-current  circuit. 
(R43a)     Put  in  a  shunt  and  regulate  until  the  proper 

current  is  obtained. 

(R43b)  Use  the  proper  regulator  for  controlling 
the  magnetism  of  the  field  for  a  varying  load. 

(B)  Series  motor  on  a  constant-potential  circuit. 


DISEASES  OF  DIEECT-CURRENT  DYNAMOS        289 

(R44c)     Put  in  a  resistance  to  cut  down  the  current. 
(R44d)     Use    the    proper    regulator    or     controlling 

switch. 
(R44e)     Change    to    an    automatic    speed-regulating 

motor. 

(44)  Shunt  motor. 

(A)  Regulator  or  field  rheostat  not  properly  set. 

(B)  Voltage  too  high. 

(R44a)     Adjust   the   regulator    or    field    rheostat    to 

control  the  speed. 
(R44b)     Use    the    proper    voltage    and    the    proper 

rheostat. 

324.  Speed  Too   Low. — 

(45)  Same  as  number  (42). 
(R45a)     Same  as  (R42). 

(46)  Overloaded. 

(R46a)     See  (Rlla)  to  (Rllg). 

(47)  Short-circuit  in  the  armature. 
(R47a)     See  (R12a)  to  (R12d). 

(48)  Striking  or  rubbing  of  the  armature  on  pole  pieces. 
(R48a)     See  (R35a)  and  (R35b). 

(49)  Friction. 

(R49a)     See  section  (321). 

(50)  Weak  magnetic  field. 

(R50a)     See  (RlOa),  (RlOb)  and  (RIOc). 

325.  Motor  Stops. — 

(51)  Too  great  an  overload.   See  (D),  (E),  (F),  and  (G) 
under  number  (11). 

(R51a)  Open  the  switch,  locate  the  trouble,  and  re- 
move. Keep  the  switch  open  and  the  arm  of  the 
rheostat  in  the  position  "off"  while  locating  and  re- 
pairing trouble.  Then  close  the  switch  and  move 
the  arm  gradually  to  the  position  "on"  to  see  if 
everything  is  correct.  With  a  series  motor,  no 
great  harm  will  result  from  motor  stopping  or 
failing  to  start.  If  it  is  a  shunt  motor  on  a  con- 
stant-potential circuit,  the  armature  may  and  prob- 
ably will  burn  out  or  the  fuse  blow. 

(52)  Very  excessive  friction. 

(R52a)     Same  as   (R51a).     See  section   (321). 


290  PRACTICAL  APPLIED  ELECTRICITY 

(53)  Circuit  open. 

(A)  Safety  fuse  melted. 

(B)  Broke  wire  or  connection. 

(C)  Brushes  not  in  contact. 

(D)  Switch  open. 

(E)  Current  fails  or  is  shut  off  from  the  station. 
(R53a)     Open  the  switch,  locate  and  repair  the  trou- 
ble, and  then  put  in  the  fuse.     See  (Rile). 

(R53b)  Open  the  switch,  locate  and  repair  the  trou- 
ble. See  (13). 

(R53c)  Open  the  switch  to  repair  the  fault.  See 
number  (3). 

(R53d)  Close  the  switch,  but  before  doing  so  see 
that  the  starting  resistance  is  in  circuit. 

(R53e)  Open  the  switch,  return  the  starting  lever 
to  the  position  "off,"  wait  for  the  current,  testing 
from  time  to  time  by  closing  the  switch  and  moving 
the  starting  lever  to  the  first  closed-circuit  position. 

(54)  Complete  short-circuit  of  the  field. 

(R54a)  Test  for  the  fault  and  repair  if  possible. 
Inspect  the  insulation  of  the  binding  posts  and 
brush  holders.  Poor  insulation,  oil,  dirt,  or  copper 
dust  may  cause  a  short-circuit.  See  number  (12). 

(55)  Complete  short-circuit  of  armature. 
(R55a)     Same  as  (R54a). 

(56)  Complete  short-circuit  of  switch. 
(R56a)     Same  as   (R54a). 

326.  Motor  Runs  Backward  or  Against  the   Brushes. — 

(57)  Wrong  connections  within  the  motor. 

(R57a)  Connect  up  properly,  referring  to  the  proper 
diagram.  If  proper  diagram  is  not  to  be  had,  try 
reversing  the  connections  to  the  brush  holders. 
Other  changes  may  be  made  until  proper  connec- 
tions are  found  for  rotation  desired,  then  connect 
up  permanently. 

327.  Dynamo  Fails  to  Generate. — 

(58)  Reversed  residual  magnetism. 

(A)     Reversed  current  in  the  field  coils. 

(R58a)  Send  a  current  from  another  machine  or 
from  a  battery  through  the  field  coils  in  the  proper 


DISEASES  OF  DIRECT-CURRENT  DYNAMOS        291 

direction  to  correct  the  fault.  Polarity  may  be 
tested  by  a  compass  needle.  If  the  connections  of 
the  windings  are  not  known,  try  one  and  test;  if 
not  correct,  reverse  connections,  try  again,  and  test. 

(B)  Reversed  connections. 

(R58b)  Connect  up  properly  for  rotation  desired, 
referring  to  the  proper  diagram  of  the  connections. 
See  that  connections  for  series  coils  (in  compound 
dynamo)  are  properly  made  as  well  as  those  for  the 
shunt  coils.  See  number  (57). 

(C)  Earth's  magnetism. 
(R58c)     Same  as  (R58a). 

(D)  Proximity  of  another  dynamo. 
(R58d)     Same  as  (R58a). 

(E)  Brushes  not  in  the  proper  position. 

(R58e)  Shift  the  brushes  until  evidence  of  an  im- 
provement is  given.  The  position  of  the  brushes 
for  best  generating  power  should  be  clearly  under- 
stood, and  is  generally  at  or  near  the  neutral  point. 

(59)  Too  weak  residual  magnetism. 
(R59a)     Same  as  (R58a). 

(60)  Short-circuit  in  the  machine. 

(R60a)     See  numbers   (12),   (54),   (55)  and   (56). 

(61)  Short-circuit  in  the  external  circuit. 

(R61a)  Lamp  socket  or  other  part  of  the  line  short- 
circuited  or  grounded  may  prevent  building  up  of 
shunt  or  compound  machines.  Locate  and  remedy 
the  fault  before  closing  switch.  See  numbers  (54), 
(55),  and  (56). 

(62)  Field  coils  opposed  to  each  other. 

(R62a)  Reverse  the  connections  of  one  of  the  field 
coils  and  test.  Compass  should  show  pole  pieces  of 
opposite  polarity.  If,  after  such  a  trial,  dynamo  does 
not  build  up,  try  (R58a).  If  the  polarity  does  not 
then  come  up  in  proper  direction,  cross  the  field 
connections  or  remagnetize  them  in  the  opposite 
direction.  See  number  (58A). 

(63)  Open  circuit. 

(A)  Broken  wire. 

(B)  Faulty  connections. 

(C)  Brushes  not  in  contact. 


292  PRACTICAL  APPLIED  ELECTRICITY 

(D)  Safety  fuse  melted  or  broken. 

(E)  Switch  open. 

(F)  External  circuit  open. 

(R63a)     Locate  and  repair  brake.     See  number  (13). 
(R63b)     See  (R58b). 
(R63c)     See  (R5a)  and  (R5b). 
(R63d)     See  (R53a). 
(R63e)     Close  the  field  switch. 

(R63f)  Test  out  and  repair  with  the  dynamo  switch 
open  until  the  repairs  are  completed. 

(64)  Too  great  a  load  on  the  dynamo. 

(R64a)  Reduce  the  load  to  pilot  lamps  alone  (shunt 
or  compound  machine).  After  dynamo  comes  up  to 
full  voltage,  as  shown  by  pilot  lamps,  or  voltmeter, 
close  the  other  circuits  in  succession  and  regulate 
the  voltage  at  the  same  time.  See  (Rlla). 

(65)  Too  much  resistance  in  the  field  regulator  or  field 
rheostat. 

(R65a)  Gradually  turn  the  regulating  switch  to  cut 
out  the  resistance  and  watch  the  pilot  lamp  or  volt- 
meter when  the  dynamo  comes  up  to  voltage,  regu- 
late, etc. 

32IB.  General  Suggestions  and  Precautions. — Never  use  ice 
or  water  to  cool  off  the  bearings,  as  it  may  get  into  the 
armature  and  ruin  it,  unless  it  has  been  made  waterproof  as 
in  the  case  of  street-car  motors. 

Never  shut  down  because  of  hot  box  until  remedies  for 
troubles  (25),  (26),  (28),  and  (32)  have  been  tried  and  proved 
useless.  If  absolutely  necessary  to  shut  down,  get  the  belt 
off  as  soon  as  possible.  Do  not  allow  shaft  to  "stick"  in 
stopping.  Get  the  boxes  or  bearings  out  and  cool  them  off 
naturally  as  soon  as  possible  and  not  in  water,  as  this  may 
ruin  them.  Then  scrape,  fit,  polish,  clean  the  shaft,  and  test 
for  free  turning  by  hand  before  belting  up  and  starting  again. 

Cleanliness  about  a  dynamo  or  motor  is  imperative.  Dirt, 
oil,  or  copper  dust  may  prove  a  source  of  great  annoyance  or 
damage.  Small  tools,  bolts,  or  pieces  of  iron  must  be  kept 
away  from  a  dynamo  as  they  may  be  drawn  into  or  fall  upon 
armature  and  ruin  it.  It  is  always  best  not  to  allow  loose 
articles  of  any  kind  to  be  placed  upon  any  portion  of  a  dynamo. 


DISEASES  OF  DIEECT-CUEEENT  DYNAMOS        393 

Brass  or  copper  oil  cans  are  best  to  use  as  they  are  non- 
magnetic. 

All  the  connections  must  be  large,  clean,  and  firm.  Look 
over  and  tighten  the  loose  connections,  screws  or  bolts,  daily. 

Always  keep  copper  brushes  raised  from  the  commutator 
when  the  dynamo  is  at  rest.  Poor,  cheap  oil  is  poor  economy. 
Use  none  but  the  best  of  mineral  oils.  All  new  oils  should 
always  be  filtered  before  using. 

Keep  cotton  waste  off  the  commutator.  Use  canvas  or 
cloth  to  wipe  the  commutator. 

A  piece  of  pine  makes  a  good  burnisher  to  use  on  the 
commutator  to  keep  it  clean  and  smooth. 


CHAPTEE  XV 

ELECTRIC  LIGHTING 

329.  The  Electric  Lamp. — The  electric  lamp  in  its  broadest 
sense  consists  of  a  part  of  an  electric  circuit  heated  to  incan- 
descence,  together   with    special   regulating    and    controlling 
devices.    Electric  lamps  may  be  conveniently  classified  under 
three  heads,  viz, 

(a)  Arc  lamps       (sections  330  to  333,  inclusive). 

(b)  Glow  lamps     (sections  334  to  339,  inclusive). 

(c)  Vapor  lamps    (sections  340  to  344,  inclusive). 

330.  The  Carbon   Arc   Lamp. — If  the  ends  of  two  carbon 
rods  that  are  connected  to  some  source  of  electrical  energy 
be  touched  together  and  then  drawn  apart,  there  will  be  an 
electric  arc  formed  between  them.     This   arc   consists  of  a 
column  of  very  hot  vapor  which  serves  to  conduct  the  elec- 
tricity from  the  end  of  one  rod  to  the  other.     The  terminals 
of  the  two  rods  will  be  wasted  away  as  the  arc  continues  to 
burn,  the  two  rods,  however,  are  not  consumed  at  the  same 
rate  always.     If  the  arc  be  formed  by  a  direct  current,  the 
ends  of  the  carbons  assume  a  form  similar  to  that  shown  in 
Fig.  238,  the  end  of  the  positive  becoming  concave,  and  the 
end  of  the  negative  pointed.     The  carbon  rod  forming  the 
positive  terminal  of  the  arc  is  consumed  approximately  twice 
as  fast  as  the  rod  forming  the  negative  terminal.     The  cup 
or  concave  portion  of  the  positive  carbon  is  called  the  crater; 
it  is  extremely  hot  and  the  greater  part  of  the  light  the  arc 
emits   comes   from  this   crater.     The   point  of  the   negative 
carbon   is   not  nearly  so  hot  as  the   crater  of  the   positive 
carbon,   and  it   does  not  emit  nearly   so  much  light.     As   a 
result  of  this  difference  in  light  emitted  by  the  positive  and 
the  negative  terminals  of  the  direct-current  arc,  the  positive 
carbon  will  be  placed  above  the  negative  so  that  the  light  will 
be    cast    downward,    except   in    special    cases;    in    the    case 

294 


ELECTRIC  LIGHTING 


295 


of  searchlights  and  projecting  lanterns,  the  arc  is  arranged 
as  shown  in  Fig.  239.  If  the  electric  arc  be  formed  by  an 
alternating  current,  the  ends  of  both  carbons  are  heated  about 
the  same,  the  upper  carbon  being  perhaps  a  little  hotter  than 
the  lower,  due  to  the  upward  movement  of  the  heated  vapor. 
As  a  result  of  the  heating  of  the  ends  of  the  two  carbons 
being  approximately  equal,  the  light  emitted  from  them  will 
be  approximately  the  same.  The  two  carbons  of  an  alternat- 


Fig.  238 


Fig.  239 


Fig.   240 


ing  current  are  wasted  away  approximately  the  same,  the 
upper  one  being  consumed  a  little  faster  than  the  lower  one. 
An  alternating-current  arc  is  shown  in  Fig.  240.  The  light 
emitted  by  the  alternating-current  arc  lamp  is  not  steady,  but 
pulsates  in  value  with  the  change  in  the  value  of  the  alter- 
nating current,  there  being  two  pulsations  of  the  light  for 
each  cycle  of  the  current. 

A  direct-current  arc  makes  practically  no  noise  when  it 
is  operating  properly,  while  the  alternating-current  arc  makes 
a  loud  humming  noise  on  account  of  the  continuous  con- 
traction and  expansion  of  the  heated  vapor,  due  to  the  varia- 
tion in  the  value  of  the  current,  and  the  lamp  mechanism 
often  vibrates,  due  to  reversals  in  magnetism. 

A  carbon  arc  lamp  consists  of  two  carbon  rods,  which  have 
their  distance  apart  controlled  by  a  suitable  mechanism  that 
is  operated  by  solenoids,  or  by  hand. 

331.  Regulation  of  Arc  Lamps  on  Constant-Voltage  and 
Constant-Current  Circuit. — If  an  electric  arc  be  connected 
directly  to  a  constant-voltage  line,  it  will  be  impossible  to 
maintain  the  arc  unless  a  resistance  be  connected  in  series 
with  the  arc  for  the  following  reason.  Assuming  the  arc  is 
operating  satisfactorily  on  a  constant-voltage  line  and  that 
the  current  decreases  in  value,  due  to  an  increase  in  length 


396  PRACTICAL  APPLIED  ELECTRICITY 

Df  the  arc,  caused  by  the  ends  of  the  carbon  being  consumed, 
this  decrease  in  current  will  cause  a  decrease  in  the  size  of 
the  arc  unless  an  additional  voltage  be  applied  at  the  termi- 
nals of  the  arc,  but  the  required  increase  in  voltage  is  not 
available  since  the  arc  is  operating  on  a  constant-voltage 
circuit  and,  as  a  result,  the  lamp  would  go  out  almost  in- 
stantly, or  before  the  regulating  mechanism  has  a  chance 
to  act  and  bring  the  carbons  nearer  together.  When  the 
circuit  is  once  broken  at  the  arc,  the  ends  of  the  carbons 
must  be  placed  in  contact  with  each  other  and  then  drawn 
apart  to  re-establish  the  arc. 

If  the  current  producing  the  arc  is  increased  in  value, 
there  will  be  an  increase  in  the  size  of  the  arc  or  a  de- 
crease in  its  resistance  and  the  constant  voltage  applied  to 
the  terminals  of  the  arc  would  be  more  than  sufficient  to 
produce  the  desired  current  and,  as  a  result,  the  current  would 
continue  to  increase  in  value  and  would  become  excessive 
almost  instantly,  or  before  the  regulating  mechanism  has 
time  to  operate  and  thus  separate  the  carbons. 

By  placing  a  resistance  in  series  with  the  arc,  an  increase 
in  current  will  cause  an  increase  in  drop  over  this  resistance 
and  a  decrease  in  current  will  cause  a  decrease  in  drop.  If 
the  resistance  is  large  enough  in  value,  the  change  in  the 
drop  over  the  resistance  will  more  than  balance  the  varia- 
tion in  the  drop  over  the  arc  caused  by  a  change  in  the  cur- 
rent, and  the  operation  of  the  arc  will  be  quite  stable.  A 
resistance  used  for  the  purpose  just  described  is  called  a 
ballast.  The  ballast  for  alternating-current  arc  lamps  is 
usually  a  reactance  coil,  instead  of  a  resistance,  the  react- 
ance coil  being  formed  by  winding  a  coil  on  a  laminated  iron 
core. 

When  arc  lamps  are  operated  on  constant-current  circuits, 
no  ballast  is  required,  as  the  current  remains  constant  re- 
gardless of  the  position  of  the  carbons,  it  being  governed  by 
the  generator,  transformer,  or  regulator.  The  drop  in  poten- 
tial over  the  arc,  however,  must  be  regulated  in  a  series  lamp 
by  means  of  a  solenoid  which  controls  the  distance  between 
the  carbons. 

332.  Multiple  Arc  Lamps. — Multiple  arc  lamps  require  only 
one  solenoid  for  their  operation.  When  the  lamp  is  first 
started,  there  is  a  large  current  in  the  circuit,  the  solenoid 


ELECTRIC  LIGHTING 


297 


is  energized  and  draws  the  carbons  apart  until  the  decrease 
in  current  due  to  the  increase  in  resistance  of  the  arc  weak- 
ens the  solenoid  to  such  an  extent  that  it  no  longer  acts  to 
separate  the  carbons.  If  the  current  decreases  in  value,  the 
solenoid  is  weakened,  which  allows  the  ends  of  the  carbons 
to  approach  each  other  and  the  current  is  restored  to  its 
original  value,  or  if  the  current  increases  in  value,  the  solenoid 
acts  to  separate  further  the  ends  of  the  carbons  and  thus  pre- 
vent an  excessive  increase  in  current. 
The  circuit  of  a  multiple  direct-current 
arc  lamp  is  shown  in  Fig.  241.  The 
circuit  is  composed  of  the  ballast  or 
steadying  resistance  (R),the  two  regu- 
lating solenoids  (Sj)  and  (S2),  and  the 
arc  (A)  between  the  ends  of  the  car- 
bons. The  steadying  resistance  and 
the  solenoids  are  so  constructed  that 
the  number  of  turns  in  circuit  can  be 
varied  by  changing  a  connection  from 
one  tap  to  another  on  the  various 
coils.  The  armature  (B),  controlled 
by  the  solenoids,  actuates  the  upper 
carbon,  the  lower  being  stationary. 
The  upper  carbon  is  connected  to  the 
positive  terminal  of  the  circuit. 

333.  Series  Arc  Lamps. — In  this 
type  of  arc  lamp  no  ballast  or  react- 
ance is  required  in  series  with  the  arc 
since  the  lamps  are  connected  in 
series  and  operate  on  a  constant-cur- 
rent circuit.  The  series  lamp  does  not 

regulate  automatically,  as  the  multiple  lamp  does,  and  a 
second  solenoid  whose  winding  is  connected  in  parallel  with 
the  arc  is  required.  The  mechanical  action  of  this  second 
solenoid  is  just  opposite  that  of  the  solenoid  connected  in 
series  with  the  arc.  The  diagram  of  a  series  arc  lamp  is 
shown  in  Fig.  242.  When  the  lamp  is  first  connected  in  the 
circuit,  the  two  terminals  are  connected  by  means  of  three 
paths — one  through  the  starting  resistance  (SR),  and  the  cut- 
out (CO);  a  second  through  the  series  coil  (C),  adjusting 
resistance  (AR)  and  arc  in  series;  and  the  third  through  the 


Fig.  241 


298 


PRACTICAL  APPLIED  ELECTRICITY 


winding  of  the  coil  (DC),  which  is  called  the  differential  shunt 
on  account  of  its  winding  being  in  shunt  with  the  arc  and  its 
action  differential  with  respect  to  the  series  coil.  The  two 
terminals  of  the  lamp  may  be  connected  directly  together 
by  closing  the  switch  (S)  which  is  usually  located  in  the 
top  of  the  lamp. 

The  operation  of  this  lamp, 
which  is  typical  of  all  series  arc 
lamps,  is  as  follows:  The  series 
solenoid  is  energized  as  soon  as 
the  lamp  is  connected  in  circuit, 
and  the  action  of  this  solenoid 
will  draw  the  ends  of  the  car- 
bons apart,  starting  the  arc  and 
opening  the  cut-out  (CO).  As 
the  carbons  are  drawn  apart,  the 
arc  voltage  increases  and  the 
current  in  the  shunt  solenoid 
(DC)  increases,  and  its  action 
tends  to  bring  the  carbons  to- 
gether, but  it  does  not  overcome 
the  action  of  the  series  coil 
(SC),  which  tends  to  separate 
the  carbons.  As  a  result  of 
these  two  solenoids  acting  at  the 
same  time,  the  arc  is  adjusted  so 
that  it  takes  a  definite  current, 
and  a  definite  voltage  exists 

across  it.  When  the  carbons  are  consumed,  the  shunt  solenoid 
brings  them  nearer  together,  as  its  current  has  increased,  due 
to  the  increase  in  voltage  over  the  arc,  and  the  current  in  the 
series  coil  remains  approximately  constant.  This  action  con- 
tinues until  the  cut-out  (CO)  is  closed  and  the  current  is 
shunted  through  it.  The  shunt  solenoid  (DC)  is  short-cir- 
cuited by  the  cut-out  closing  and  there  is  no  current  in  the 
series  solenoid  (SC),  the  upper  carbon  is  released  and  the  two 
come  together.  When  the  end  ot  the  two  carbons  come  to- 
gether, the  current  is  re-established  in  the  series  solenoid  and 
the  lamp  again  picks  up.  If  the  carbons  be  entirely  consumed, 
the  cut-out  remains  closed  and  the  circuit  of  which  the 


Fig.  242 


ELECTEIC  LIGHTING  299 

lamp  is  a  part  is  not  opened,  even  though  the  lamp  is  not 
operating.  A  dash  pot  (DP)  dampens  the  movement  of  the 
armature  of  the  solenoids,  which  greatly  improves  the  opera- 
tion of  the  lamp.  In  some  types  of  series  arc  lamps  the 
shunt  and  series  windings  are  both  placed  on  the  same 
spool  instead  of  on  two  different  ones,  as  shown  in  Fig.  242. 

334.  Glow  Lamp.— In  all  glow  lamps  the  light  is  emitted 
from  a  solid  electrical  conductor  that  is  heated  by  an  elec- 
trical current  to  such  a  temperature  that  it  emits  light.    The 
lamps  included  under  this  head  are  the  ordinary  carbon-fila- 
ment   lamps,    the    different    metal-filament    lamps,    such    as 
tungsten  and  tantalum,  and  the  Nernst  lamp. 

335.  Carbon-Filament  Lamp. — The  common  carbon-filament 
incandescent    lamp    consists    of    a    fine    filament    of    carbon 
mounted  in  a  highly  exhausted  glass  bulb,  which  may  assume 
a  number  of  different  forms,  depending  upon  the  particular 
use  of  the  lamp.     The  carbon  filament  is  connected  to  the 
external  circuit  by  means  of  two  short  pieces   of  platinum 
that  are  embedded  in  the  glass.     Platinum  is  used  for  mak- 
ing  these    connections    on    account   of   it   being   capable    of 
withstanding   a   high   temperature  and   it   contracts   and   ex- 
pands  due   to   changes   in   temperature   the   same   as   glass, 
which  is  quite  an  advantage  in  maintaining  the  vacuum  in 
the  bulb  containing  the  filament. 

The  method  usually  employed  in  the  manufacture  of  the 
carbon  filament  is  as  follows:  Some  of  the  fibrous  sub- 
stances such  as  cotton  are  thoroughly  cleansed  and  then  dis- 
solved in  a  solution  of  zinc  chloride  by  constant  stirring, 
forming  a  thick  fluid  which  is  freed  from  lumps  by  filtering 
and  from  bubbles  by  heating  almost  to  the  boiling  point  under 
pressure.  This  fluid  is  then  "squirted"  through  a  small  hole 
and  allowed  to  pass  into  an  alcohol  bath,  which  immediately 
hardens  the  gelatinous  rod  which  can  then  be  thoroughly 
washed  in  water.  This  thread  has  the  appearance  of  celluloid, 
it  is  fairly  tough,  and  may  be  cut  into  lengths  and  bent  on 
formers  into  any  shape  desired.  They  are  then  packed  in 
charcoal  and  carbonized  in  a  furnace,  after  which  they  are 
mounted  on  the  platinum  wires  that  are  to  form  the  terminals 
and  heated  electrically  by  a  current  to  a  high  temperature  in  a 
vapor  of  hydrocarbon.  The  hydrocarbon  vapor  is  decomposed 
by  the  hot  filament,  which  results  in  a  deposit  of  carbon  on 


300 


PRACTICAL  APPLIED  ELECTRICITY 


the  filament.  This  deposit  will  be  greatest  at  the  hotest 
points  in  the  filament,  which  will  be  at  the  points  of  highest 
resistance,  or  smallest  cross-section  and,  as  a  result,  the  fila- 
ment is  made  more  uniform  in  cross-section,  and  its  resist- 
ance slightly  lowered,  due  to  the  increase  in  area.  The  above 
process  is  called  flashing.  The  completed  filament  is  placed 
in  a  glass  bulb,  which  is  exhausted  by  means  of  special 
pumps  and  sealed.  A  mounting  suitable  to  screw  into  a 
lamp  socket  is  then  mounted  on  the  bulb  and  the  terminals 
of  the  filament  connected  to  the  two  parts  of  the  mount- 
ing, which  make  electrical  contact  with  the  two  terminals  of 
the  line  when  the  lamp  is  screwed  into  the  socket. 

The  resistance  of  a  carbon  filament  when  working  under 
normal  conditions  is  approximately  half  what  it  is  at  ordi- 
nary temperatures. 

336.  Metalized  Carbon-Filament  or 
Gem  Lamp. — The  filaments  used  in  the 
so-called  metalized  carbon-filament 
lamps  are  carbon  filaments  that  have 
been  subjected  to  an  enormously  high 
temperature,  both  before  and  after 
flashing,  by  means  of  a  specially  con- 
structed electric  furnace.  The  term 
"metalized"  is  used  on  account  of  the 
filaments  acquiring  a  positive  tempera- 
ture coefficient  when  subjected  to  very 
high  temperatures. 

337.  Tantalum  Lamp. — The  tantalum 
lamp  was  invented  by  Dr.  Bolton — 
chemist  for  Siemens  and  Halske — who 
discovered  the  peculiarities  of  tantalum 
and  the  methods  of  obtaining  the  pure 
metal.  Tantalum  is  obtained  by  special 

processes  from  the  ores  tantalite  and  columbite,  the  tantalite 
being  found  principally  in  Australia  and  the  columbite  in 
New  England.  Filaments  of  the  desired  size  are  drawn  from 
the  pure  ductile  tantalum.  The  melting  temperature  of  tan- 
talum is  approximately  2800°  centigrade  and  its  resistance 
increases  with  a  rise  in  temperature.  The  tensile  strength 
of  tantalum  is  very  high  when  cold,  but  when  heated  it  be- 
comes soft  and  after  the  filament  has  been  burning  a  few 


Fig.  243 


ELECTEIG  LIGHTING  301 

hours  it  becomes  very  brittle,  which  is  the  great  disadvan- 
tage of  this  kind  of  a  filament.  The  filament  of  a  tantalum 
lamp  to  operate  on  a  110-volt  circuit  is  a  great  deal  longer 
than  the  carbon  filament,  and  special  means  must  be  provided 
for  mounting  those  long  filaments,  such  as  shown  in  Fig.  243. 

The  tantalum  lamp  gives  a  much  whiter  light  than  the 
carbon-filament  lamp  on  account  of  the  high  temperature 
at  which  it  operates.  The  life  of  a  tantalum  lamp  is  a  great 
deal  less  on  an  alternating-current  circuit  than  it  is  on  a 
direct-current  circuit  and  its  life  on  an  alternating-current 
circuit  depends  upon  the  frequency. 

338.  Tungsten  Lamp. — The  latest  form  of  metallic-filament 
lamp  placed  on  the  market  is  the  tungsten  lamp.  It  has  only 
been  commercially  used  for  about  three  years,  but  even  in 
that  short  time  it  has  attained  the  highest  position  in  the 
field  of  incandescent  lighting. 

Tungsten  is  not  a  rare  metal,  having  been  used  for  a  num- 
ber of  years  in  the  manufacture  of  tool  steel  and  armor 
plate.  Owing  to  the  fact  that  as  hitherto  produced  the  metal 
was  very  hard  and  brittle,  it  has  not  until  recently  been 
obtained  in  a  ductile  form  and  consequently  was  not  drawn 
into  wire  as  was  tantalum.  It  has  a  very  high  melting  point 
—about  3050° C. — which  allows  the  lamps  to  be  operated  at 
the  relatively  high  efficiency  of  1.25  w.p.c.  and  even  higher. 
This  makes  the  light  emitted  very  much  nearer  a  pure  white 
than  any  other  incandescent  lamp  which  has  yet  come  into 
commercial  use. 

There  are  four  methods  of  forming  the  tungsten  filament, 
but  the  one  in  most  general  use  in  this  country  is  the  Auer, 
or  paste,  process.  This  process  starts  with  a  pure  tungstic 
acid,  obtained  from  some  one  of  the  various  tungsten  ores, 
such  as  wolframite  or  scheelite.  Tungstic  acid  is  a  yellow 
powder,  which  must  undergo  several  processes  of  purifica- 
tion and  reduction  before  it  is  finally  reduced  to  the  pure 
metal.  This  metal  is  used  in  the  form  of  a  fine  black  pow- 
der, which  is  mixed  with  a  binding  material  in  order  to 
form  a  putty-like  mass  that  can  be  squirted  through  a  very 
small  die,  even  as  small  as  one-thousandths  of  an  inch.  A 
die  is  very  expensive,  being  made  from  a  diamond,  through 
which  a  hole  is  drilled  with  a  fine  flexible  steel  needle.  Its 
life  is  very  short  on  account  of  the  wear  which  the  hard 


302 


PRACTICAL  APPLIED  ELECTRICITY 


metal  gives  the  diamond  and  the  enormous  pressure  of  30000 
pounds  per  square  inch,  under  which  the  filament  is  formed. 
Thus  only  enough  filaments  for  1500  lamps  can  be  formed 
before  the  die  is  so  badly  worn  that  it  must  be  rebored  for 
the  next  larger  size  filament,  an  operation  which  costs  al- 
most as  much  as  a  new  die. 

The  filament  while  being  squirted  is  looped  back  and  forth 
on  a  card,  which,  when  filled,  is  laid  aside  to  allow  the  fila- 
ment time  to  dry.  After  drying,  the  filaments  are  cut  into 
loops,  which  resemble  in  shape  the  finished  filaments.  These 
loops  are  placed  in  a  tube  furnace  and  baked  at  a  cherry  red 
heat  in  an  atmosphere  of  gas  which  contains  no  oxygen. 
After  baking  for  some  time  the  more  volatile  constituents 
of  the  binder  are  found  to  have  been  driven  off  and  the  fila- 
ments are  ready  to  be  "formed." 

_  They    are    now    connected    into    an 

electrical  circuit  by  means  of  clips 
and  are  gradually  heated  in  an  at- 
mosphere of  inert  gas,  until  incan- 
descence is  reached,  when  the  re- 
maining binding  material  is  volatil- 
ized, leaving  the  pure  metal  fila- 
ment. This  last  process  causes  the 
filament  to  shrink  somewhat,  which, 
however,  has  been  allowed  for  in  the 
previous  operations. 

The    formed    filament    is    now 

mounted  on  the  center  support  and  the  two  ends  are  welded 
to  the  supporting  wires  in  an  atmosphere  of  forming  gas. 
After  sealing  the  mount  into  the  tubulated  bulb,  the  lamp 
follows  practically  the  same  process  of  exhaustion  as  the 
tantalum  lamp. 

There  has  been  recently  discovered  a  means  whereby  tungs- 
ten is  rendered  ductile,  and  wire-drawn  filaments  are  the  re- 
sult. Tungsten  wire  has  a  tensile  strength  varying  from 
400  000  to  600  000  pounds  per  square  inch,  a  value  three  to 
four  times  that  attained  by  tantalum  wire.  This  wire  can  be 
bent  into  any  form  and  consequently  can  be  mounted  in  such 
a  manner  as  to  be  more  capable  of  withstanding  shocks  than 
was  possible  with  a  filament  made  by  the  paste  process. 


Glower 
Fig.  244 


ELECTEIC  LIGHTING 


303 


EDI80N  •***! 


339.  Nernst  Lamp.  —  The  filament  or  glower  of  a  Nernst 
lamp  consists  of  a  small  rod  of  porcelain-like  material  com- 
posed of  the  oxides  of  zirconium  and  yttrium.  This  rod  is  a 
good  insulator  at  ordinary  temperatures,  but  becomes  a  very 
good  conductor  at  a  low  red  heat,  and  its  resistance  decreases 
very  rapidly  as  the  temperature  rises.  If  such  a  glower  is 
to  be  used  some  means  must  be  provided  for  heating  it  until 
it  will  become  a  conductor  in  starting  the  lamp,  and  a  bal- 
last resistance  must  be  cdn- 
nected  in  series  with  the 
glower  to  prevent  the  current 
becoming  excessive  after  the 
glower  has  started  to  con- 
duct. A  diagram  of  a  single 
glower  lamp  is  shown  in  Fig. 
244.  When  the  lamp  is  first 
connected  to  the  line,  the  cir- 
cuit is  completed  through  the 
heater  coil  and  cut-out.  As 
the  temperature  of  the  glow- 
er  is  raised,  due  to  the  action 
of  the  heater,  its  resistance 
is  lowered,  which  permits  the 


ARMATURE  SUPPORT 

L.POST 

—  BALLAST 
CUT  OUT  COIL 
—  ARMATURE 

••^T^C: SILVER  CONTACT  STOP 
-— HOUSING 

"CONTACT  SLEEVE  PORCELAIN 

GLOBE  HOLDING  SCREW 

HOLDER  PORCELAIN 
HEATER  PORCELAIN 
HEATER  TUBE 


Fig.  243 


electricity  to  pass  through 
the  glower,  ballast,  and  cut- 
out coil  all  in  series.  After  a  short  time  this  current  will 
reach  a  value,  due  to  decrease  in  the  resistance  of  the  glower, 
sufficient  to  operate  the  cut-out  and  thus  disconnect  the  heater, 
and  the  glower  will  become  incandescent.  The  ballast  is  com- 
posed of  fine  iron  wire  placed  inside  of  an  exhausted  glass 
tube  to  prevent  the  iron  oxidizing  when  it  is  heated.  This 
ballast  increases  in  resistance  with  an  increase  in  tempera- 
ture, due  to  an  increase  in  current  and,  as  a  result,  automat- 
ically tends  to  maintain  the  current  constant.  A  Nernst  lamp 
is  shown  complete  in  Fig.  245. 

340.  Vapor  Lamp. — In  the  different  forms  of  vapor  lamp 
the  light  is  emitted  from  an  incandescent  or  luminescent 
column  of  vapor  that  conducts  the  electricity.  The  lamps 
included  under  this  head  are  the  flaming-arc  lamps,  mercury- 
vapor  lamps,  and  the  Moore  tube. 


304  PRACTICAL  APPLIED  ELECTRICITY 

341.  Flaming   Arc. — In   the   carbon   arc   lamp   the   greater 
part  of  the  light  is  emitted  from  the  ends  of  the  intensely 
heated   carbons,   the   arc   itself   emitting   only   a   pale   violet 
light.     If  the  carbons  between  which  the  arc  is  formed  be 
impregnated  with  metallic  salts,  or  rods  of  metal,  or  metal 
oxide  be  used  instead  of  carbon,  an  arc  will  be  formed  which 
is  highly  charged  with  metal  vapor.     The  light  emitted  by 
such  an  arc  comes  mostly  from  the  incandescent  particles  in 
the  metal  vapor,   very   little  coming  from  the  terminals  ot 
the  rods  forming  the  arc.    Arc  lamps  employing  impregnated 
carbons  or  metal  rods  instead   of  carbons  to  form  the  arc 
are  known  as  flaming  arcs. 

One  of  the  materials  most  commonly  used  in  combination 
with  carbon  is  calcium,  which  gives  the  light  emitted  by  the 
arc  a  highly  brilliant  yellow  color.  Carbons  impregnated 
with  stroncium  give  a  red  light,  and  those  impregnated  with 
titanium  or  barium  give  a  white  light.  There  are  many 
different  forms  of  electrodes  for  the  flaming  arc  lamps,  con- 
sisting of  different  metals  and  combinations. 

342.  Bremen  Flaming-Arc  Lamp. — The  Bremer  lamp  is  one 
of  the  oldest  and  is  the  most  efficient  of  the  different  flam- 
ing arc  lamps  on  the  market.    The  carbons  in  this  lamp  are 
placed  parallel  or  slightly  inclined  to  each  other,  instead  of 
being  placed  in  the  same  plane  with  their  axes  coinciding, 
which  results  in  a  larger  arc  being  formed  between  them. 
This  arrangement  of  the  carbons  gives  the  lamp  an  additional 
advantage   over  the   other   arrangement,   since   there   is   no 
lower  carbon  in  the  path  of  maximum  illumination.     In  the 
construction  of  the  lamp,  a  magnet  is  provided  which  creates 
a  magnetic  field  that  acts  on  the  arc  and  deflects  it  down- 
ward, thus  preventing  its  climbing  up  the  carbons,  and  at  the 
same   time    giving   a    longer    and    larger    arc    and    a    better 
distribution. 

343.  Mercury-Vapor  Lamp. — The  mercury-vapor  lamp  con- 
sists  of  a  highly  exhausted   glass   tube   with   two   platinum 
wires  sealed  in  its  ends.     One  of  these  wires  is  connected 
inside  the  tube  to  a  piece  of  iron  or  graphite  that  forms  the 
anode  and  the  other  is  connected  to  a  pool  of  mercury  that 
forms  the  cathode.     In  starting  such  a  lamp  a  high  electro- 
motive  force   or  a   special   starting   device   is  required,   but 
after  the  lamp  is  once  started  a  current  of  several  amperes 


ELECTRIC  LIGHTING 


305 


can  be  easily  maintained  by  a  pressure  of  from  30  to  100 
volts.  The  mercury  vapor  in  the  tube  gives  off  a  bright 
light  that  is  deficient  in  the  longer  wave-lengths,  or  red.  The 
lack  of  the  longer  wave-lengths  results  in  an  unpleasant 
distortion  of  color. 

The  lamp  may  be  started  by  tilting  the  tube,  it  being  nor- 
mally at  an  angle  to  the  horizontal,  which  allows  the  mercury 
to  extend  from  one  end  to  the  other  and  complete  the  cir- 
cuit, and  the  circuit  is  maintained  through  the  mercury  vapor 
when  the  metallic  mercury  circuit  is  broken  by  the  tube  be- 


Fig.  246 


ing  allowed  to  return  to  its  normal  position.  A  spark  may  be 
caused  to  pass  through  the  tube,  due  to  the  action  of  an  in- 
duction or  kick  coil  which  ruptures  the  medium  and  starts 
the  lamp.  A  third  means  of  starting  is  to  place  an  auxiliary 
positive  electrode  near  the  negative  electrode  to  be  used  in 
starting  and  the  connection  is  then  transferred  to  the  other 
positive  electrode  after  the  lamp  is  started. 

The  lamp  is  operated  on  alternating  current  by  connect- 
ing the  negative  electrode  of  the  lamp  to  the  middle  point 
of  a  transformer  winding  and  having  two  positive  electrodes 
located  at  the  same  end  of  the  tube  and  connected  to  the 


306 


PRACTICAL  APPLIED  ELECTRICITY 


two  ends  of  the  transformer  winding.    A  mercury-vapor  lamp 
is  shown  complete  in  Fig.  246. 

344.  Moore  Tube. — The  Moore  tube  resembles  the  mer- 
cury-vapor lamp  in  that  it  consists  of  a  conducting  vapor  en- 
closed in  a  glass  tube  and  the  light  is  emitted  from  incan- 
descent particles  in  the  vapor  stream.  The  tube  from  which 
the  light  is  emitted  may  be  of  any  length  up  to  about  200 
feet,  of  any  desired  form,  and  its  diameter  may  be  as  large 
as  1%  inches.  Two  graphite  electrodes  are  sealed  in  the 
ends  of  this  tube,  which  is  filled  with  air,  carbon  dioxide, 
nitrogen,  or  other  suitable  gas.  The  secondary  winding  of  a 


Fig.  247 


Fig.  248 


transformer  is  connected  to  the  graphite  terminals  in  the 
ends  of  the  tube,  the  primary  winding  being  connected  to 
the  source  of  power,  as  shown  in  Fig.  247.  The  vacuum  in 
the  tube  becomes  more  and  more  perfect,  which  decreases 
the  efficiency  of  the  lamp,  and  some  means  must  be  provided 
for  regulating  the  vacuum,  which  is  done  as  follows:  A 
separate  tube  (t)  projects  downward  from  the  main  one, 
as  shown  in  Fig.  247,  and  is  connected  with  what  is  called  a 
feeder  valve.  This  feeder  valve,  shown  more  in  detail  in 
Fig.  248,  consists  of  a  solenoid  connected  in  series 
with  the  primary  winding  of  the  transformer.  The  iron 
plunger  (I)  is  fastened  in  a  glass  displacement  tube  and  it 
is  raised  or  lowered,  due  to  a  change  in  the  current  in  the 
solenoid.  In  the  end  of  the  tube  (t)  there  is  cemented  a 
carbon  plug  with  a  very  small  opening  in  it,  which  is  nor- 


ELECTKIC  WIRING  307 

mally  covered  with  mercury.  If  the  displacing  tube  be  moved 
up,  due  to  the  action  of  the  solenoid,  the  mercury  recedes, 
uncovering  the  opening  in  the  carbon  plug  and  allowing  a 
small  amount  of  gas  to  enter  the  tube. 

With  an  increase  in  vacuum  there  is  a  decrease  in  resist- 
ance and  an  increase  in  current  in  the  secondary  winding 
of  the  transformer,  and  also  a  corresponding  increase  in 
current  in  the  primary  winding.  This  increase  in  current 
causes  the  feeder  valve  to  operate  and  the  vacuum  is  re- 
stored to  normal  by  admitting  gas.  The  secondary  voltage 
required  will  depend  upon  the  length  of  the  main  tube. 

345.  Units  of  Illumination. — The  luminous  intensity  of  a 
source  of  light  is  measured  by  comparing  it  with  a  source  of 
unit  intensity,  and  the  unity  commonly  employed  for  meas- 
uring luminous  intensity  is  the  candle-power.  The  unit  of 
candle-power  is  equal  to  1.111  hefner  units. 

The  Hefner  lamp,  so-called  from  its  inventor,  is  a  specially 
constructed  lamp  that  burns  pure  amyl  acetate.  The  wick 
and  the  tube  holding  the  wick  are  of  definite  dimensions  and 
in  using  the  lamp  the  wick  is  adjusted  so  that  the  flame  is 
a  prescribed  height.  The  intensity  of  a  beam  of  light  in  a 
horizontal  plane  from  such  a  lamp  is  called  a  hefner  unit  or  a 
hefner. 

The  illumination  or  the  amount  of  light  falling  on  an  ob- 
ject is  measured  in  a  unit  called  the  foot-candle.  A  foot- 
candle  is  the  normal  illumination  produced  by  one  unit  of 
candle-power  at  a  distance  of  one  foot. 

The  mean  horizontal  intensity  is  the  average  intensity  in 
all  directions  in  a  horizontal  plane  that  passes  through  the 
source  of  light.  In  the  case  of  incandescent  lamps  this  plane 
is  taken  perpendicular  to  the  axis  of  the  lamp. 

The  mean  spherical  candle-power  is  the  average  candle- 
power  taken  in  all  directions  around  the  source  of  light. 

346.  Photometry. — The  measurement  of  light  emitted  by 
a  lamp  is  called  photometry.  This  is  always  accomplished 
by  comparing  the  beam  of  light  from  a  given  lamp  with  the 
beam  of  light  from  a  standard  lamp,  and  the  device  used  for 
making  this  comparison  is  called  a  photometer.  The  inten- 
sity in  different  directions  can  be  measured  by  placing  the 
lamp  in  different  positions  with  respect  to  the  photometer. 
Lighting  measurements  are  all  based  upon  the  law  of  in- 


308 


PRACTICAL  APPLIED  ELECTRICITY 


verse  squares,  which  can  be  explained  by  reference  to  Fig. 
249.  A  source  of  light  is  shown  at  (L)  and  four  rays  of 
light  (Ri),  (R2),  (R3),  and  (R4)  are  shown  emanating  from 
(L)  and  forming  a  pyramid.  Three  cross-sections  through 
this  pyramid  and  perpendicular  to  its  axis  are  shown  at  (A), 
(B),  and  (C).  These  three  cross-sections  and  the  light  (L) 
are  all  equally  spaced  and,  as  a  result,  the  cross-section  (B) 
is  four  times  that  of  (A),  and  (C)  is  nine  times  that  of  (A), 
etc.,  or  the  cross-sections  between  the  four  rays  increase  as 
the  square  of  the  distance  the  cross-sections  are  from  the 
source  of  light.  Since  the  same  total  number  of  rays  pass 
through  each  area,  the  intensity  per  unit  of  area  varies  in- 


Fig.  249 


x, 


Fig.  250 


versely  as  the  square  of  the  distance  from  the  source  of  light. 

The  Bunsen  photometer  is  one  of  the  oldest  and  simplest 
forms  of  photometers  and  also  one  of  the  most  efficient  means 
of  comparing  the  intensities  of  different  sources  of  light.  The 
construction  of  this  photometer  can  best  be  explained  by  ref- 
erence to  Fig.  250.  A  sheet  of  white  paper,  the  center  por- 
tion of  which  is  made  transparent  by  being  treated  with 
paraffin  or  some  other  similar  substance,  is  mounted  inside 
a  box  (B),  as  shown  in  the  figure.  This  sheet  of  paper  is 
called  the  screen  (C)  of  the  photometer. 

The  two  sides  of  this  screen  are  viewed  simultaneously 
through  the  sight  piece  (S)  by  the  aid  of  the  two  mirrors 
(Mj)  and  (M2)  which  are  so  mounted  that  they  make  an  angle 
of  about  140  degrees  with  each  other  and  equal  angles  with 
the  plane  of  the  screen.  The  light  falling  on  either  side  of 


ELECTRIC  LIGHTING  309 

this  screen  is  not  all  reflected,  a  part  passing  through  the 
translucent  spot  in  the  center.  •  When  the  illumination  on 
both  sides  of  the  screen  is  the  same,  an  equal  amount  of 
light  is  transmitted  through  the  screen  in  both  directions, 
and  if  the  lights  on  the  two  sides  are  of  the  same  hue  the 
spot  in  the  center  and  the  remainder  of  the  screen  should 
appear  of  the  same  color. 

The  photometer  is  used  as  follows:  Two  lamps,  whose  in- 
tensities are  to  be  compared,  are  located  a  known  distance 
apart  on  what  is  known  as  the  photometer  bench.  The  box 
(B),  Fig.  250,  is  placed  between  the  two  lamps  so  that  its 
axis  (XiXo)  coincides  with  the  line  connecting  the  cen- 
ters of  the  two  sources  of  light  and  so  arranged  that  it  can 
be  moved  along  this  line.  It  is  then  moved  until  the  two 
parts  of  the  screen  have  the  same  appearance.  When  this 
balance  is  obtained,  the  distance  the  center  of  each  source 
of  light  is  from  the  screen  is  determined  and  the  relation 
of  the  intensities  is  calculated  by  applying  the  law  of  inverse 
squares  given  above.  If  the  candle-power  of  one  lamp  is 
known,  the  candle-power  of  the  other  one  can  be  easily  de- 
termined, as  follows: 

Let  (Ss)  represent  the  candle-power  of  the  standard  lamp. 

Let  (Sx)  represent  the  candle-power  of  the  lamp  being 
tested. 

Let  (Ds)  represent  the  distance  the  screen  is  from  the 
standard  lamp. 

Let  (Dx)  represent  the  distance  the  screen  is  from  the  lamp 
being  tested. 

Sx        DS2 
Then 

Ss         DX2 

DS2 
and  Sx=      —  Ss  (126) 


347.  The  Specific  Consumption  of  Lamps.  —  The  specific 
consumption  of  a  lamp  in  practice  is  always  specified  by  giv- 
ing the  watts  consumed  in  the  lamp  per  spherical  candle- 
power  of  light  emitted.  The  specific  consumption  of  different 
types  of  lamps  is  given  in  Table  X. 


310  PRACTICAL  APPLIED  ELECTRICITY 

TABLE  NO.  X. 

APPROXIMATE    SPECIFIC    CONSUMPTION  OF  DIFFERENT  TYPE 

LAMPS 

Watts  per  Mean 
Spherical  Candle- 
Type  of  Lamp —  Power  Remarks 

Direct-current    series 1.0 

Direct-current    multiple 2.4 

Alternating-current    series...  1.7  No  outer  globe 

Alternating-current    multiple. 2. 5  No  outer  globe 

D.  C.  Bremer  flaming  arc...   .196  48  volts  over  arc 

A.  C.  Bremer  flaming  arc...   .226  48  volts  over  arc 

Carbon-filament   lamps 3.0     to  3.5 

Tantalum  lamps 1.8      to  2.2 

Tantalum    lamps 1.8  Direct  current 

Tungsten     1.25 

Nernst    2.95  Six  glower 

Nernst    3.92  Single  glower 

Mercury-vapor     48*  See  note  (A) 

Moore  tube   1.7*  See  note  (B) 

Note  (A) :  The  candle-power  is  measured  perpendicular 
to  the  axis  of  the  tube. 

Note  (B) :  This  value  corresponds  to  a  vacuum  in  the 
tube  of  approximately  .10  millimeters  of  mercury. 

348.  Distribution  Curves. — The  distribution   of  light  from 
a  source  through  any  plane  and  in  different  directions  can 
be  represented  graphically,  and  such  a  graphical  representa- 
tion is  called  a  distribution  curve.     The   distribution  curve, 
about  a  four-candle-power  lamp  in  a  vertical  plane,  is  shown 
in  Fig.  251.     The  intensity  in  different  directions  being  pro- 
portional to  the  distance,  the  curve  is  from  the  center.    The 
form  of  the  filament,  bulb,  shades,  and  reflectors  all  have  an 
influence  in  determining  the  shape  of  the  distribution  curve. 

349.  Calculation     of    illumination. — If    a     16-candle-power 
lamp  (L)  be  placed  8  feet  from  the  plane  (A),  as  shown  in 
Fig.  252,  the  illumination  per  unit  area  on  the  plane   (A)   at 
the  point   (B)   would  be  equal  to   (16-^-82)   =  14  foot-candle, 
since   the   intensity   varies    inversely   as   the    square    of   the 
distance.     In  general,  to  get  the  illumination  at  any   given 


*Watts  per  candle-power. 


ELECTEIC  LIGHTING 


311 


point,  the  candle-power  in  the  direction  measured  must  be 
divided  by  the  square  of  the  distance  from  the  light  to  the 
point  illuminated. 

When  the  surface  illuminated  is  not  at  right  angles  to  the 
light,  the  values  of  illumination  obtained  above  must  be  mul- 
tiplied by  a  reduction  factor,  which  takes  into  account  the 
angle  at  which  the  rays  of  light  strike  the  surface,  Thus, 


~Fis.  251 

if  a  lamp  (V)  be  placed  8  feet  above  the  horizontal  plane 
(H),  as  shown  in  Fig.  253,  and  it  is  desired  to  determine 
the  illumination  at  the  point  (B),  6  feet  from  the  vertical 
line  through  the  lamp,  you  should  proceed  as  follows:  The 
distance  (0  the  point  (B)  is  from  the  lamp  is  equal  to 


I  =   V/V2  +  h2 

The  value  of  (?)  in  Fig.  253  is  equal  to 
1=  V82  +  62  =  10 

Assuming  the  intensity  of  the  light  from  the  lamp  (L)  along 
the  line  (I)  is  20  candle-power,  then  the  illumination  on  a 
surface  (P)  at  the  point  (B)  perpendicular  to  the  line 
(I)  would  be  equal  to 

20         1 

Illumination  = =  —  foot-candle 

102        5 


PRACTICAL  APPLIED  ELECTRICITY 


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ELECTEIC  LIGHTING 


313 


The  illumination  of  }£  foot-candle  on  the  surface  (P)  is  to 
be  distributed  over  a  larger  area  when  the  horizontal  plane 
is  considered.  The  ratio  of  the  illumination  per  unit  of  area 
on  the  horizontal  plane  to  the  il- 
lumination per  unit  area  on  the 
plane  (P)  is  equal  to  the  inverse 
ratio  between  a  unit  area  in  the 
plane  (P)  and  the  projection  of  this 
unit  area  on  the  horizontal  plane. 
This  ratio  is  equal  to  the  cosine  of 


ft 8  Feet 

I 


B 


/B7 

Fig.  252  Fig.  253 

the  angle  between  the  plane  (P)  and  the  horizontal  plane, 
which  is  the  same  as  the  angle  between  (I)  and  a  vertical 
line  through  the  lamp.  The  constants  by  which  the  intensity 
in  candle-power  along  the  line  (0  must  be  multiplied  to 
obtain  the  illumination  on  the  horizontal  for  different  values 
of  (h)  and  (v)  are  given  in  Table  No.  XI.  The  illumination 
on  the  horizontal  plane  for  the  above  example  would  be 
equal  to 

20  X    .008  015  =  .1603   foot-candle 

When  the  source  of  light  consists  of  a  number  of  lamps,  the 
illumination  for  each  lamp  can  be  determined  and  the  re- 
sultant illumination  obtained  by  addition. 

TABLE    NO.   XII 

REQUIRED  ILLUMINATION  FOR  VARIOUS  CLASSES  OF  SERVICE 

Intensity  of 
Illumination 
Class  of  Service  in  Foot-Candles 

General  illumination  of  residences 1    to    2 

Reading  1    to    3 

Auditoriums   and    theaters 1     to     4 

Churches  2     to     4 

Bookkeeping  and  clerical  work 3     to     5 

General  illumination  of  stores 2     to     5 

Engraving  and  drafting 5     to  10 

Street  lighting  by  electricity 05  to      .06 


314 


PRACTICAL  APPLIED  ELECTRICITY 


The  illumination  required  for  various  classes  of  service  is 
given  in  Table  No.  XII. 

350.  Shades,  Reflectors,  and  Diffusers.— Often  the  distribu- 
tion from  a  source  of  light  is  undesirable  and  the  intrinsic 
brilliancy  of  the  source  may  be  too  great  for  the  best  effect 


135* 


150° 


Fig.  254 


or  greatest  comfort,  which  results  in  the  use  of  shades,  re- 
flectors and  diffusers.  A  shade  is  used  to  modify  the  light 
and  is  placed  between  the  source  and  the  eye.  It  may  act 

as  a  reflector  or  diffuser.  A 
reflector  serves  to  re-direct 
the  light  and  thus  change 
the  distribution,  and  it  may 
act  as  a  shade  in  certain 
directions.  A  diffuser  is 
intended  to  decrease  the 
intrinsic  brilliancy  and  to 
reduce  the  glare,  and  in  so 
doing  act  as  a  shade  or 
reflector.  The  arc  lamp  is 
usually  enclosed  in  two 
globes  when  used  for  in- 
terior lighting,  in  order  to  reduce  the  intrinsic  brilliancy.  The 
change  in  shape  of  the  distribution  curve,  shown  in  Fig.  251, 
due  to  the  use  of  a  holoplane  reflector,  is  shown  in  Fig.  254. 
The  reflector  and  lamp  are  shown  in  Fig.  255. 

351.     The    Effect    Different   Colored    Walls    Have    Upon    the 
General     Illumination. — In    rooms    not    larger    than    approxi- 


Fig.  255 


ELECTRIC  LIGHTING  315 

mately  15  feet  by  15  feet,  the  color  of  the  walls  will  have 
considerable  effect  upon  the  general  illumination  when  the 
lamps  are  used  without  shades  or  reflectors.  The  effective 
illumination  in  rooms  with  different  colored  walls  is  obtained 
by  multiplying  the  illumination  given  directly  by  the  lamp 
by  the  factor  given  in  Table  No.  XIII. 

TABLE  NO.  XIII 
FACTORS   FOR   OBTAINING  EFFECTIVE   ILLUMINATION 

Illumination 
Color  Wall  Factor 

White  paper 3.3 

Orange  paper. 2.0 

Yellow   paper 1.67 

Yellow   painted  wall 1.67 

Pink  paper  (light) 1.56 

Green  paper  (emerald) 1.22 

Brown  paper  (dark) 1.15 

Blue-green  paper 1.14 

Chocolate  paper   (deep) 1.04 


CHAPTER  XYI 

ELECTRIC  WIRING 

352.  Wiring    in    General. — The    term    "electric    wiring"    is 
usually  considered  to  mean  the  proper  placing  of  electrical 
conductors  to  form  a  complete  metallic  circuit  for  conducting 
the  electrical  energy  to  and  from  the  points  where  it  is  gen- 
erated and  consumed.     The  above  use  of  the  term,  however, 
is   rather   narrow   and   it   should   include   in   addition   to    the 
proper  placing  of  the  electrical  conductors,  the  calculation  of 
the  proper  size  of  conductors  to  meet  given  requirements;  the 
selection   of   the   proper    materials;    a    consideration    of   the 
proper   location   of   the   service    mains,    meters,    outlets    for 
lamps,  panel  boards,  switches,  controlling  devices,  etc.,  and  a 
thorough  understanding  of  the  requirements  of  the  inspection 
department  under  whose  jurisdiction  the  work  is  being  done. 

353.  Factors    Determining    the    Size    of    Conductors. — The 
problem  in  electric  wiring  is  the  transmission  of  a  certain 
amount  of  energy  from  one  point  to  another,  and  it  is  usually 
desired  that  this  transmission  be  effected  with  a  minimum 
loss  and  at  the  same  time  keep  the  initial  cost  within  a  rea- 
sonable value. 

The  drop  in  electrical  pressure  between  any  two  points 
connected  by  an  electrical  conductor  is  equal  to  the  product 
of  the  current  in  the  conductor  connecting  the  two  points  and 
the  resistance  of  the  conductor,  or  volts  drop  equals  (R  X  I). 
This  drop  in  pressure  in  volts  multiplied  by  the  current  in 
amperes  gives  the  value  of  the  power  loss  in  watts  in  the 
conductor,  or  power  loss  in  watts  equals  (R  X  I)  times  (I), 
which  equals  (I2R).  The  current  in  a  conductor  forming  part 
of  the  circuit  connecting  a  given  load  to  its  source  of  energy 
is  fixed  by  the  voltage  of  the  generator  and  the  resistance 
of  the  load.  Since  the  value  of  the  current  in  the  expression 
for  the  power  loss  in  a  conductor  is  to  be  fixed  for  any  given 

316 


ELECTRIC  WIRING  317 

voltage,  the  only  way  to  reduce  the  loss  is  to  reduce  the  value 
of  the  resistance  (R). 

The  resistance  of  a  conductor  composed  of  a  given  material 
and  at  a  constant  temperature  varies  directly  as  the  length 
and  inversely  as  the  cross-sectional  area.  The  length  of  a 
conductor  connecting  a  load  and  generator  is  usually  deter- 
mined by  the  distance  between  them  (in  some  cases  the 
conductor  may  be  a  great  deal  longer  than  this  distance  on 
account  of  its  not  following  a  direct  path),  and,  as  a  result,  the 
resistance  can  be  reduced  only  by  an  increase  in  the  cross- 
section  of  the  conductor.  An  increase  in  cross-section,  the 
length  remaining  constant,  means  a  like  increase  in  weight, 
and  hence  an  increase  in  cost.  The  loss  in  the  conductors 
in  any  circuit  may  be  made  very  small  by  an  increase  in  their 
cross-sections,  but,  as  pointed  out  above,  the  cost  of  the  con- 
ductors is  increasing  at  the  same  time  the  loss  is  decreasing. 
In  practice,  a  reasonable  loss,  usually  expressed  in  per  cent, 
is  allowed  and  the  size  of  the  conductor  required  to  carry  the 
current  is  figured  from  this  value. 

Neglecting  the  loss  in  the  conductors,  there  is  another 
important  factor  to  consider  in  the  determination  of  the 
proper  size  of  conductors  to  use,  and  that  is  the  allowable 
rise  in  temperature  of  the  conductor  caused  by  the  loss  in 
it.  The  rise  in  temperature  due  to  a  given  loss  will  depend 
upon  the  rate  at  which  the  heat  generated  in  the  conductor 
is  radiated,  which  in  turn  will  depend  upon  its  insulation  and 
mechanical  protection.  The  allowable  current-carrying  ca- 
pacity for  different  size  copper  wires  has  been  established 
by  the  Underwriters,  and  Table  G,  Chapter  20,  gives  a 
complete  set  of  these  values.  It  must  be  understood  that 
the  percentage  drop  in  voltage  is  not  taken  into  account  in 
this  table. 

In  some  cases  the  size  of  the  conductor  is  determined  by 
the  mechanical  requirements;  it,  however,  should  never  be 
smaller  than  the  size  determined  by  the  electrical  require- 
ments. 

354.  Choice  of  Material  to  Use  as  a  Conductor. — From  the 
standpoint  of  loss  in  the  line,  the  choice  of  a  material  to  use 
as  a  conductor  is  governed  by  its  resistance.  In  order  that 
the  loss  be  small,  the  specific  resistance  must  be  low.  This, 
however,  does  not  mean  that  the  materials  of  lowest  specific 


318  PRACTICAL  APPLIED  ELECTRICITY 

resistance  will  be  used,  as  their  cost  may  be  a  great  deal 
more  than  that  of  some  material  having  a  higher  specific 
resistance.  If  the  specific  resistance  of  a  material  which  we 
shall  caH  (A)  is  twice  that  of  a  material  which  we  shall  call 
(B),  and  the  cost  of  the  material  (A)  per  unit  volume  is 
just  one-half  that  of  material  (B),  then  the  cost  of  the  two 
conductors,  one  each  of  the  (A)  and  (B)  materials,  of  the 
same  length  and  having  the  same  resistance,  will  be  the  same. 
As  far  as  the  loss  in  the  conductors  and  the  initial  cost  are 
concerned,  there  would  be  no  choice  in  the  above  case.  The 
conductor  composed  of  material  (A)  would  be  larger  than 
the  one  composed  of  material  (B),  and  more  material  would 
be  required  to  insulate  it;  a  larger  conduit  would  be  required 
to  accommodate  it  if  it  be  placed  in  a  conduit;  and  it  would 
be  bulkier  and  more  than  likely  harder  to  handle.  The  tensile 
strength  of  one  material  might  be  such  that  it  would  not 
meet  the  mechanical  requirements  although  it  fulfills  the 
electrical  requirements.  Thus  a  long  span  across  a  stream 
would  be  made  of  steel  wire  on  account  of  its  high  tensile 
strength  and  not  for  electrical  reasons.  The  material  that 
seems  to  meet  best  all  the  requirements  for  a  conductor, 
except  in  special  cases,  is  copper,  and  for  this  reason  copper 
is  usually  used.  The  supply  of  copper  and  its  cost  are  also  in 
its  favor  as  compared  to  silver,  which  is  electrically  better. 

355.  Calculation  of  the  Resistance  of  a  Conductor. — The 
resistance  of  any  conductor  (neglecting  changes  in  tempera- 
ture) can  be  determined  if  its  dimensions  and  the  value  of  the 
specific  resistance  of  the  material  composing  it  are  known. 
The  equation  used  in  making  this  calculation  is 

Kl 

R  — -  (127) 

d2 

In  the  above  equation  (K)  represents  the  mil-foot  resistance, 
or  it  is  the  resistance  of  a  portion  of  the  conductor  one  foot 
in  length  and  having  a  circular  cross-section  one-thousandth 
of  one  inch  in  diameter;  (I)  is  the  length  of  the  conductor 
in  feet;  and  (d)  is  the  diameter  of  the  conductor  in  mils  (the 
mil  is  equal  to  the  one-thousandth  part  of  one  inch). 

Example. — Calculate  the  resistance  of  a  conductor,  com- 
posed of  commercial  copper  having  a  mil-foot  resistance  of 


ELECTEIC  WIEING  319 

(10.8),  500  feet  in  length,  and  having  a  diameter  of  325.  mils. 
(This  corresponds  to  a  No.  0,  B.  &  S.  gauge  wire). 

Solution. — Substituting  in  equation  (127),  the  values  of  (K), 
(t)  and  (d)  given  in  the  problem,  gives 
10.8  X  500 

R  =  —       =  .05112 

325  X  325 

Ans,     .05112  ohm. 

If  the  length  of  a  circuit  is  given,  the  value  of  (Z)  to  sub- 
stitute in  equation  (127)  is  equal  to  twice  the  length  of  the 
circuit;  or  if  the  length  of  the  circuit  be  represented  by  the 
letter  (L)  the  value  of  (I)  is  equal  to  (2L). 

356.  Calculation  of  Size  of  Conductor  When  Allowable  Drop 
and  Current  Are  Given. — If  the  drop  in  potential  (E),  in  volts, 
that  is  to  occur  in  any  circuit  when  there  is  a  definite  cur- 
rent in  the  circuit,  and  the  current  of  (I)  amperes  are  both 
given,  the  resistance  of  the  circuit  in  ohms  is  equal  to 

E 
R  =  —  (128) 

I 

Knowing  the  resistance  of  the  circuit  and  its  length,  the  size 
of  the  conductors  required  can  be  determined  by  substituting 
in  the  following  equation: 

I  X  K  X  2L 
d2  = (129) 


Since  from  equation 


and  from  equation  (127) 


320  PRACTICAL  APPLIED  ELECTRICITY 

i 
and 

I  X  K  X  2L 


E 

Example.  —  The  voltage  at  the  terminals  of  a  generator  is 
112  volts,  and  it  is  desired  to  transmit  50  amperes  over  a 
circuit  450  feet  in  length  with  a  drop  in  voltage  not  to  exceed 
two  per  cent.  What  size  of  conductor  is  required  if  it  be 
composed  of  copper  having  a  mil-foot  resistance  of  10.8? 

Solution.  —  Tbe  drop  in  voltage  (E)  is  equal  to  two  per  cent 
of  112,  or 

E  =  .02  X  112  =  2.24  volts 

Substituting  the  value  of  (E)  just  obtained,  and  the  value  of 
(I),  (L),  and  (K)  in  equation  (129),  gives 
50  X  10.8  X  2  X  450 


2.24 
Solving  this  equation,  gives 

d2  =  215  170 
and 

d  =  464  mils 

Referring  to  a  table  giving  the  diameters  of  different  size  wire 
you  will  find  a  No.  0000  B.  &  S.  gauge  is  the  size  having 
a  diameter  practically  the  same  as  the  value  just  obtained. 
In  case  the  value  of  (d)  obtained  is  less  than  the  diameter  of 
a  No.  14  wire,  the  No.  14  wire  should  always  be  used,  or  in 
no  case  use  a  wire  smaller  than  No.  14,  B.  &  S.  gauge,  except 
in  the  wiring  of  fixtures. 

Tables  L,  M,  and  N,  Chapter  20,  give  the  proper  size 
conductors  to  use  on  50-,  110-,  and  220-volt  circuits,  when 
the  distance  to  the  center  of  distribution  and  the  current  the 
conductor  is  to  carry  are  given,  the  loss  in  each  case  being 
two  per  cent.  The  following  example  will  illustrate  the  use 
of  the  tables: 

Example.  —  A  current  of  100  amperes  is  to  be  supplied  to  a 
number  of  incandescent  lamps  from  a  generator  whose  ter- 
minal voltage  is  220  volts  with  a  loss  not  to  exceed  two  per 
cent.  What  size  conductor  should  be  used  when  the  gen- 
erator and  lamps  are  200  feet  apart? 

Solution.  —  Referring    to    Table    N,    Chapter    20,    and    pass- 


ELECTRIC  WIEING  321 

ing  along  the  horizontal  lire  corresponding  to  100  amperes 
until  you  strike  the  vertical  column  headed  200,  which  cor- 
responds to  the  distance  to  the  center  of  distribution,  you 
will  find  that  a  No.  0  B.  &  S.  gauge  wire  is  the  proper  size 
to  use. 

In  some  cases  the  percentage  loss  to  be  allowed  in  the  line 
may  be  different  from  that  given  in  the  tables,  and  the  size 
wire  can  be  determined  as  follows:  The  percentage  loss 
allowed  should  be  divided  by  two,  giving  a  constant  which 
we  shall  call  (C).  Then  determine  the  size  wire  required  by 
means  of  the  tables,  on  the  assumption  that  the  loss  is  two 
per  cent,  divide  the  circular-mil  area  of  the  wire  thus  obtained 
by  the  constant  (C),  and  look  up  the  size  of  wire  having  a 
circular-mil  area  corresponding  to  or  next  larger  than  this 
result. 

Example. — It  is  desired  to  transmit  100  amperes  from  a 
220-volt  generator  a  distance  of  200  feet  with  an  allowable 
loss  of  five  per  cent.  What  size  wire  should  be  used? 

Solution. — The  constant  (C)  is  equal  to  5  divided  by  2,  or 

C  =  5  -f-  2  =  2.5 

Referring  to  Table  N,  Chapter  20,  we  find  that  a  No.  00 
B.  &  S.  gauge  wire  would  be  required  if  the  loss  were  only 
two  per  cent.  The  circular-mil  area  of  a  No.  00  B.  &  S. 
gauge  wire  is,  from  Table  C,  equal  to  133  100,  and  this  value 
divided  by  (C),  or  2.5,  gives  the  circular-mil  area  of  the  wire 
to  be  used. 

Circular-mil  area  =  133  100  ~  2.5  =  53  240 
diameter  =  230.7  mils 

A  No.  3  B.  &  S.  gauge  wire  has  a  diameter  of  229.4  mils, 
so  that  it  should  be  used. 

357.  Motor  Wiring  Formula. — The  size  of  wire  required  to 
supply  energy  to  a  direct-current  motor  can  be  calculated 
as  follows:  Assuming  the  horse-power,  efficiency,  and  the 
voltage  of  the  motor  are  given,  the  current  that  must  be  sup- 
plied when  the  motor  is  operating  under  full  load  can  be 
determined  by  substituting  in  the  following  equation: 

h.p.  X  746         100 

1  =  —  -X (130) 

E  F 


322  PRACTICAL  APPLIED  ELECTRICITY 

In  the  above  equation  (h.p.)  represents  the  horse-power  of 
the  motor,  (E)  the  voltage  the  motor  is  designed  to  operate 
on,  (F)  the  efficiency  of  the  motor  in  per  cent,  and  (746)  is 
the  number  of  watts  per  horse-power.  Having  determined 
the  value  of  the  current  (I),  the  size  of  wire  required  can  be 
determined  as  in  section  (356).  The  size  of  conductor  used 
should  be  such  as  to  allow  for  a  25  per  cent  overload  on  the 
motor,  the  current  in  the  conductor  not  exceeding  the  values 
given  in  Table  G,  Chapter  20. 

Example. — A  50-horse-power  direct-current  motor  is  to  be 
supplied  with  current  from  a  220-volt  generator  over  a  line 
250  feet  in  length  and  having  such  a  resistance  that  the  drop 
in  voltage  shall  not  exceed  4  per  cent.  What  size  wire  should 
be  used,  the  efficiency  of  the  motor  being  90  per  cent? 

Solution. — Substituting  directly  in  equation  (130)  gives 

50  X  746        100 

I  =  — - —     -  X  — —  =  188.  +  amperes 
220  90 

When  the  motor  is  carrying  a  25  per  cent  overload  the  cur- 
rent in  the  leads  will  be  equal  to  1.25  times  188,  or 

Overload  current  =  1.25  X  188  =  235  amperes 

Since  the  maximum  value  of  current  given  in  Table  N, 
Chapter  20,  is  less  than  235  amperes,  the  size  wire  can  be  cal- 
culated as  follows:  The  size  of  wire  required  to  carry  235 
amperes  with  a  4  per  cent  drop  will  be  the  same  as  the  size 
of  wire  required  to  carry  117.5  amperes  with  a  2  per  cent 
drop.  Referring  to  Table  N,  we  find,  that  with  a  current  of 
120  amperes  and  a  distance  of  250  feet,  a  No.  000  B,  &  S. 
gauge  wire  is  required.  Referring  to  Table  G,  we  find  that 
No.  000  B.  &  S.  gauge  wire  cannot  be  used  to  carry  235  am- 
peres except  when  insulations  other  than  rubber  are  used. 
The  size  of  wire  required,  if  it  is  insulated  with  rubber,  would 
be  a  300  000  circular-mil  cable. 

358.  Methods  of  Wiring  and  Rules  Governing  Same. — The 
rules  and  requirements  governing  the  proper  installation  of 
electrical  conductors  and  the  kind  of  material  that  must  be 
used  vary  in  different  localities.  In  the  majority  of  cases 
the  rules  and  requirements  of  the  National  Board  of  Fire 
Underwriters  as  published  in  the  National  Electric  Code  are 


ELECTKIC  WIRING  323 

followed.  In  some  municipalities  there  are  certain  ordinances 
in  force,  or  the  power  company  may  have  certain  require- 
ments that  must  be  met  before  they  will  supply  electrical 
energy.  The  National  Electric  Code  should,  however,  be  fol- 
lowed at  all  times  unless  there  are  other  requirements  in 
force. 

There  is  a  supplement  to  the  National  Electric  Code  that 
contains  a  complete  list  of  all  the  fittings  that  are  approved 
by  the  Underwriters,  and  in  no  case  should  fittings  be  used 
that  do  not  appear  in  this  supplement  unless  by  special  per- 
mission. 

There  are  several  methods  of  wiring  that  are  approved  by 
the  National  Board  of  Fire  Underwriters,  viz.: 

(a)  Open,  or  exposed,  work. 

(b)  Moulding   work. 

(c)  Concealed  "knob  and  tube"  work. 

(d)  Interior  conduit  and  armored  cable  work. 

359.  Open,  or  Exposed.  Work. — This  method  of  wiring  is 
perhaps  the  cheapest  of  any  of  the  methods  given,  and  it  is 
at  the  same  time  one  of  the  safest  and  best  methods  when 
properly  installed.  It  is  used  a  great  deal  in  mills,  factories, 
etc.,  where  the  appearance  of  the  wires  on  the  ceiling  or  walls 
is  of  no  great  importance.  The  wires  used  in  this  method 
of  wiring  may  be  either  rubber  covered  or  provided  with 
slow-burning  weatherproof  insulation.  Rubber  insulation 
should  always  be  used  when  the  wire  is  in  a  damp  place,  such 
as  a  cellar,  and  either  weatherproof  or  rubber  insulation  may 
be  used  to  protect  it  against  corrosive  vapors.  When  installed 
in  dry  places  and  for  voltages  below  300,  the  wires  should 
always  be  rigidly  supported  on  non-absorptive,  non-combustible 
insulators  that  separate  them  2%  inches  from  each  other 
and  1/2  inch  from  the  surface  over  which  they  pass.  For 
voltages  from  300  to  500,  the  wires  should  be  separated  4 
inches  from  each  other  and  1  inch  from  the  surface  over 
which  they  pass.  If  the  wiring  is  in  a  damp  place,  the  wires 
should  always  be  at  least  1  inch  from  the  surface  over 
which  they  pass,  even  if  the  voltage  be  below  300  volts,  the 
other  distances  being  the  same  as  above.  The  wires  should 
always  be  protected  by  porcelain  tubes  or  short  pieces  of 
flexible  tubing  when  they  pass  over  pipes  or  other  material, 


324 


PRACTICAL  APPLIED  ELECTRICITY 


as  shown  in  Fig.  256.  It  is  usually  best  to  place  the  wires 
above  the  pipes  rather  than  under  them.  The  wires,  when 
they  run  vertically  on  the  walls,  should  be  protected  by  a 
suitable  boxing  or  run  in  a  pipe,  as  shown  in  Fig.  257.  There 
should  be  a  clearance  of  at  least  1  inch  around  the  wires 
when  they  are  placed  inside  the  box,  which  should  be  closed  at 
the  top,  and  the  holes  in  the  top  of  the  box  where  the  wires  enter 
should  be  bushed  with  porcelain  tubes.  If  the  wires  be  placed 
inside  a  pipe,  they  should  each  be  encased  in  a  piece  of  flexible 


-Gas  Pipe 


Fig.  256 


Fig.  257 


tubing  that  will  extend  from  the  insulator  below  the  end  of  the 
pipe  to  the  first  one  above  it.  Porcelain  tubes  should  -always 
be  used  when  the  wires  pass  through  walls  and  floors.  These 
tubes  should  be  long  enough  to  reach  all  the  way  through 
the  wall  or  floor,  except  in  special  cases,  when  a  piece  of  pipe 
may  be  used  with  a  long  porcelain  bushing  put  into  it  from 
each  end  and  cemented  in  place. 

360.  Moulding  Work. — In  this  class  of  work  the  wires  are 
placed  in  grooved  pieces  of  wood  that  are  provided  with  a 
wooden  cap  that  is  fastened  to  the  body  of  the  moulding  after 
the  wires  have  been  put  in  place.  The  dimensions  of  this 
moulding  are  governed  by  the  requirements  of  the  Under- 
writers, and  the  number  of  grooves  is  usually  two  or  three, 
depending  upon  whether  it  is  to  be  used  on  a  two-  or  three- 
wire  system.  The  capping  can  be  made  to  correspond  in 
design  and  color  to  the  other  woodwork  in  a  building  or 
room,  which  makes  it  less  conspicuous. 


ELECTEIC  WIEING 


325 


Moulding  work  is  extensively  used  alone  and  in  combination 
with  other  classes  of  work,  there  being  numerous  fittings  on 
the  market  that  can  be  used  in  changing  from  one  system  to 
the  other.  It  cannot  be  used  in  damp  places,  or  in  rooms 
where  it  will  be  subjected  to  fumes,  or  in  concealed  work  or 
elevator  shafts.  Approved  rubber  covered  wire  should  be 
used  when  it  is  placed  in  moulding.  The  same  precautions 
should  be  taken  in  protecting  the  wires  in  this  class  of  work 
where  they  pass  through  floors  and  ceilings  as  were  men- 
tioned for  open,  or  exposed,  work.  A  device  known  as  a 
kicking  box,  Fig.  258,  is  usually  used  in  protecting  the  wires 
at  the  points  where  they  enter  or  emerge  from  the  floor. 


Fig.  258 


Fig.  259 


Metal  mouldings,  such  as  those  shown  in  Fig.  259,  are  used 
quite  extensively  at  the  present  time,  on  circuits  requiring 
not  more  than  600  watts  and  where  there  is  a  difference  in 
potential  not  to  exceed  300  volts.  Special  fittings  must  be 
used  with  this  kind  of  moulding  so  that  it  is  continuous  both 
mechanically  and  electrically.  The  moulding  should  be 
grounded,  or  the  rules  governing  its  installation  are  prac- 
tically the  same  as  those  governing  the  installation  of  conduit 
work. 

361.  Concealed  "Knob  and  Tube"  Work.— Concealed  "knob 
and  tube"  work  is  fast  disappearing  on  account  of  the  great 
danger  of  fire  due  to  short-circuits  between  the  wires  that 
are  placed  in  the  walls  and  floors.  This  class  of  wiring  is 
quite  cheap  and  it  is  extensively  used  in  frame  buildings  in 
localities  where  the  Inspection  Departments  will  permit.  The 
wires  for  this  class  of  work  must  have  an  approved  rubber 
insulation  and  be  supported  by  means  of  knobs  or  tubes  on 


326 


PRACTICAL  APPLIED  ELECTRICITY 


the  joist  and  studding.  When  the  wires  are  run  in  a  direction 
perpendicular  to  the  direction  in  which  the  joists  run,  holes  are 
drilled  in  the  joists  and  porcelain  tubes,  with  a  shoulder  on  one 
end,  are  driven  into  these  holes,  through  which  the  wires  are 
passed,  as  shown  in  Fig.  260.  The  knobs  should  support  the 

wires  at  least  1  inch  from 
the  surface  over  which  they 
run;  these  knobs  should 
not  be  farther  apart  than 
Fig.  260  4^  feet  and  the  wires  fast- 

ened to  them  in  an  approved 

manner.  Split  knobs  are  usually  used  for  this  class 
of  work,  as  the  wires  are  no  longer  approved  by 
the  underwriters.  The  various  wires  should  be  at 
least  5  inches  apart  at  all  times  when  supported  on 
the  knobs,  and  it  is  best  to  have  the  wires 
run  on  separate  joist  or  studding  when  pos- 
sible, as  shown  in  Fig.  261.  Porcelain  tubes 
should  always  be  used  where  the  wires  pass 
through  walls  and  ceilings,  and  the  knobs 
should  be  so  located  that  there  is  no  strain 
on  the  tubes.  Each  wire  must  be  encased 
in  a  piece  of  flexible  tube  at  all  outlets, 
switches,  distributing  centers,  etc.,  and  this 
piece  of  tubing  should  be  of  sufficient  length 
to  extend  from  the  last  insulator  and  project 
at  least  1  inch  beyond  the  outlet,  as  shown  in 
Fig.  260.  When  wires  cross  pipes  or  other 
wires,  they  should  be  insulated  by  means  of 
porcelain  tubes  or  pieces  of  flexible  tubing,  as 
shown  in  Fig.  256. 

362.  Interior  Conduit  and  Armored  Cable 
Work. — Armor  cable  consists  of  rubber-covered 
wire  that  is  protected  from  mechanical  injury 
by  two  layers  of  flexible  steel  armor,  which 
also  serves  to  protect  the  wire  to  a  certain 
extent  from  dampness,  Fig.  262.  A  lead  covering 
is  often  placed  between  the  insulation  on  the  wire  and  the  steel 
armor,  which  protects  the  enclosed  conductors  from  dampness. 
Leaded  armor  cables  can  be  used  for  all  classes  of  work,  and 
the  unleaded  cable  can  also  be  used  for  all  classes  where  it 


Fig.  261 


W 


ELECTEIC  WIEING  327 

is  not  exposed  to  dampness.  Leaded  cables  may  be  buried  in 
the  walls  or  floors,  but  reasonable  care  must  be  exercised  in 
installing  the  unleaded  cable  to  protect  it  from  being  exposed 
to  moisture.  Special  fittings  are  on  the  market  for  con- 
necting the  ends  of  the  armor  to  metal  outlet  boxes.  The 
armor  should  be  cut  away  6  or  7  inches  from  the  end 
of  the  wires  so  that  switches,  fixtures,  etc.,  may  be  properly 
connected. 

In  new  work,  holes 
are  drilled  in  the  joists 
and  studding  and  the 
cable  is  pulled  into 
place,  it  being  fastened 
by  means  of  special  Fig.  262 

straps     of    metal.     Ar- 
mored cable  is  used  quite  extensively  in  the  wiring  of  old 
buildings,  as  it  can  be  put  into  different  places  regardless  of 
its  coming  in  contact  with  pipes,  etc. 

In  conduit  work  approved  rubber-covered  wire  must  be 
used  and  it  is  drawn  into  a  system  of  iron  piping  that  is 
installed  and  connected  to  all  outlet  and  cut-out  boxes  before 
the  wires  are  put  in  place.  The  conduit  must  never  have  an 
inside  diameter  of  less  than  .625  inch  and  in  installing  it  no 
bends  or  elbows  should  have  a  radius  less  than  3.5  inches, 
nor  should  there  be  more  than  the  equivalent  of  four  quarter 
bends  from  outlet  to  outlet.  The  conduits  should  be  cleaned 
out  before  the  wires  are  drawn  in  and  it  is  often  advisable 
to  blow  a  small  quantity  of  soapstone  into  them,  which  will 
reduce  the  friction  of  the  wire  on  the  surface  of  the  pipe  to 
a  minimum.  This  system  of  wiring  is  the  safest,  most  satis- 
factory, and  in  the  long  run  no  doubt  the  most  economical 
method  of  installing  wires. 

363.  Service  Wires. — When  the  electrical  energy  is  sup- 
plied from  a  source  outside  the  building,  certain  precautions 
must  be  taken  in  bringing  the  wires  into  the  building.  When 
the  wires  are  overhead  and  are  taken  into  the  building  above 
the  basement,  they  must  be  provided  with  drip  loops  and  pass 
through  insulating  tubes  in  the  wall  that  slope  so  their  out- 
side end  is  lower  than  the  inside  end.  Such  an  arrangement 
is  shown  in  Fig.  263.  When  the  wires  are  brought  into  the 
basement  from  an  outside  service  that  is  overhead,  they 


328 


PRACTICAL  APPLIED  ELECTRICITY 


should  be  placed  in  a  metal  conduit  with  its  outside  end  bent 
over  and  provided  with  a  suitable  fitting,  thus  forming  a 
drip  loop,  as  shown  in  Fig.  264.  When  the  outside  wires  are 
underground  and  are  brought  into  the  basement,  they 
should  be  placed  in  metal  or  porcelain  tubes  that  are  tightly 
sealed  afterwards.  The  leads  pass  directly  to  the  cut-out, 
then  to  the  main  switch,  both  of  which  should  be  enclosed 
in  a  suitable  cabinet,  and  from  the  switch  to  the  meter,  and 


t-Out 


Fig.  263 


Fig".  264 


then  to  the  main  distributing  center.  A  three-branch  dis- 
tributing center  for  a  three-wire  system  is  shown  in  Fig. 
265.  The  gaps  in  the  various  leads  are  for  fuses. 

364.  Location  of  Outlets,  Switches,  and  Distributing  Board. 
— The  various  distributing  boards  from  which  the  branch  cir- 
cuits emanate  should  always  be  located  as  near  the  center 
of  the  load  as  possible,  so  that  the  circuits  will  be  practically 
the  same  length.  These  boards  are  mounted  in  either  metal 
boxes  or  wooden  boxes  with  fireproof  lining,  depending  upon 
the  kind  of  work.  Each  branch  circuit  is  provided  with  a 
double-pole  switch  and  properly  fused.  A  three-wire  distrib- 
uting board  is  shown  in  Fig.  266  and  a  two-wire  board  in 
Fig.  267.  A  main  switch  and  fuses  are  placed  in  the  leads 
connecting  the  board  to  the  source  of  energy. 

The   switches   in   the   various   branch   circuits   outside   the 


ELECTEIC  WIRING 


329 


distributing  board  should  be  located  in  such  positions  that 
they  will  be  convenient  to  operate.  They  should,  as  a  rule, 
in  light  wiring  be  placed  near  a  door  and  on  the  side  nearest 
the  door  handle. 

The  location  of  the  outlets  will  depend  upon  the  location  of 
the  lamps,  kind  of  lamps — arc  or  incandescent — location  of 
motors,  etc.  A  chart  of  the  standard  symbols  for  wiring 
plans,  as  adopted  and  recommended  by  the  National  Electrical 
Contractors'  Association  of  the  United  States,  is  given  in 
Chapter  20. 


Fig.  265 


Fig.  266 


365.  Installing  Arc  Lamps  and  Fixtures. — Arc  lamps  should 
be  insulated  from  inflammable  material,  and  at  all  times  sur- 
rounded with  a  glass  globe  surrounding  the  arc  and  securely 
fastened  in  place.     Approved  rubber-covered  wire  should  be 
used  and  it  should  be  supported  on  porcelain  or  glass  insu- 
lators in  constant-current  systems  that  hold  the  wire  at  least 
1  inch  above  the  surface  over  which  the  wire  passes,  and 
these  wires  should  never  be  nearer  each  other  than  8  inches, 
except  in  cut-out  boxes  and  in  the  lamps. 

Fixtures,  when  supported  from  the  gas  piping  or  from  any 
grounded  metal  work  of  the  building,  must  be  insulated  from 
such  metal  by  an  approved  insulating  joint  placed  as  neai 
the  walls  or  ceiling  as  possible.  The  cross-section  of  an 
insulating  joint  is  shown  in  Fig.  268. 

366.  Electric   Heaters. — All  electric  heaters   must  be  pro 
tected  by  cut-out  and  controlled  by  indicating  switches.    These 


330 


PRACTICAL  APPLIED  ELECTRICITY 


switches  should  be  double  pole  except  when  the  device  con- 
trolled does  not  require  more  than  660  watts.  Heaters  must 
always  be  in  plain  sight  unless  special  permission  be  given 
by  the  Inspection  Department  having  jurisdiction.  Stationary 
heaters,  such  as  radiators,  ranges,  plate  warmers,  etc.,  must 
be  placed  in  safe  locations,  isolated  from  inflammable  ma- 
terials, and  always  treated  as  sources  of  heat. 


Fig.  267 


Fig.  2G8 


367.  Electric  Generators  and   Motors. — All  generators  and 
motors  should  be  located  in  dry  places.     They  should  never 
be  installed  in  places  where  a  hazardous  process  is  carried 
on,  in  dusty  places,  or  in  places  where  they  are  exposed  to 
inflammable  gases  or  flying  of  combustible  materials. 

Generators  and  motors  should  always  be  insulated  from  the 
surrounding  floor  on  wooden  bases.  When  it  is  impossible 
to  insulate  them  for  any  reason,  the  Inspection  Department 
having  jurisdiction  may  permit  the  omission  of  the  insulating 
frame,  in  which  case  the  frame  should  be  permanently  and 
effectively  grounded. 

368.  Electrical   Inspection. — No  attempt  has  been  made  in 
this  chapter  to  give  all  the  details  that  must  be  observed  in 
the  proper  installation  of  electrical  conductors,  it  being  left 
to  the  engineer  in  charge,  who  should  have  a  copy  of  both 
the  National  Electric  Code  and  its  supplement,  which  contains 
a   list   of   approved    fittings   and    materials.     The   Inspection 
Department  under  whose  jurisdiction  the  work  is  being  done 


ELECTKIC  WIRING  331 

should  be  consulted  freely,  as  it  will  often  save  time  and 
trouble  in  cases  where  doubtful  work  has  been  suspected,  and 
the  inspector  requires  the  floors  to  be  taken  up  or  the  plaster 
knocked  off  in  certain  places  to  satisfy  himself  that  the  work 
was  properly  done. 


*     I 


CHAPTEE  XVII 


THE    ALTERNATING-CURRENT    CIRCUIT 

369.  Definition  of  an  Alternating  Electromotive  Force  or 
Current. — An  alternating  electromotive  force  or  current  is 
one  that  changes  in  value,  and  reverses  in  direction  at  certain 
regular  intervals.  Such  an  electromotive  force  would  be 
induced  in  a  loop  of  wire  that  was  resolved  in  a  magnetic 
field,  as  shown  in  Fig.  126.  An  alternating  current  would 
exist  in  a  closed  circuit  connected  to  the  terminals  of  such  a 
coil  by  means  of  two  brushes  and  slip-rings,  as  shown  in 
Fig.  127. 

370.     Hydraulic  Analogy  of 
an    Alterating    Current. — The 

alternating  current  in  an 
electric  circuit  can  be  com- 
pared to  the  flow  of  water  in 
a  closed  pipe  connected  to  a 
cylinder  in  which  there  is  an 
oscillating  piston  operating, 
as  shown  in  Fig.  269.  If 
the  arm  (A)  be  moved  at  a 
constant  angular  velocity 

there  will  be  a  flow  of  water  through  the  pipe  similar  to  that 
represented  by  the  curve  in  Fig.  270.  The  length  of  the  hori- 
zontal line  (AB)  corresponding  to  the  time  of  one  complete 
revolution  of  the  arm  (A),  and  the  length  of  the  ordinate  of 
the  curve,  or  vertical  distance  from  a  point  on  the  line  (AB) 
to  the  curve,  at  any  instant,  represents  the  rate  at  which  the 
water  or  liquid  is  passing  a  given  cross-section  of  the  pipe, 
or  the  current  in  the  pipe. 

371.  Cycle — Frequency — Alternation — Period — Synchronism 
— Phase  Displacement. — When  an  alternating  pressure  or  cur- 

332 


Fig.  269 


THE  ALTERNATING-CURRENT  CIRCUIT 


333 


0°          90° 


ISO 
Fig.  270 


B 


270°      360° 


rent  has  passed  through  a  complete  set  of  positive  and  nega- 
tive values,  starting  from  any  value  and  again  returning  to 
that  value  in  the  same  direction,  the  pressure  or  current  has 
completed  what  is  called  a  cycle.  A  complete  cycle  is  shown 
by  curve  (E)  in  Fig.  271,  which  represents  an  alternating 
electromotive  force.  The 
e.m.f.  is  zero  at  (A),  in- 
creases to  a  maximum  posi- 
tive value  at  (C),  decreases 
to  zero  at  (D,)  and  reverses 
in  direction,  increasing  to  a 
maximum  negative  value  at 
(E),  and  then  decreases  to 
zero  at  (B),  which  completes 
the  cycle,  it  passing  through 
a  similar  set  of  values  in  the 
next  equal  interval  of  time. 

The  number  of  cycles  the  pressure  or  current  passes 
through  in  one  second  is  called  the  frequency.  Thus  a  60-cycle 
electromotive  force  or  current  would  be  one  that  parsed 
through  a  complete  set  of  positive  and  negative  values  60 
times  per  second. 

An  alternation  is  half  a 
cycle,  and  corresponds  to  a 
complete  set  of  positive  or 
negative  values  of  e.m.f.  or 
current.  There  will  be  just 
twice  as  many  alternations 
in  a  given  time  as  there  are 
cycles,  or  a  frequency  of  60 
cycles  would  mean  120  al- 
ternations per  second. 

The  period  of  an  e.m.f.  or 
current  is  the  time  in  sec- 
onds required  to  complete  one  cycle.  Thus  the  period  of  a 
60-cycle  e.m.f.  or  current  would  be  %0  of  a  second  and  of  a 
25-cycle  e.m.f.  or  current  i/£5  of  a  second. 

Two  electromotive  forces  or  currents  are  said  to  be  in 
synchronism  when  they  have  the  same  frequency. 

Any  number  of  e.m.f.'s  or  currents  are  said  to  be  in  phase 
when  they  pass  through  corresponding  values  of  their  re- 


360 


334 


PRACTICAL  APPLIED  ELECTRICITY 


0° 


90' 


D 


180°       270°  •  360° 

Fig.  272 


spective  cycles  at  the  same  time.  Thus  the  current  (I), 
and  the  e.m.f.  (E),  Fig.  271,  are  in  phase  because  they  both 
pass  through  corresponding  values  of  their  cycles  at  the  same 
time. 

Any  number  of  e.m.f. 's  or  currents  are  said  to  be  displaced 
in  phase  when  they  do  not  pass  through  corresponding  values 

of  their  respective  cycles  at 
the  same  time  Thus  the 
current  (I)  and  the  e.m.f. 
(E),  Fig.  272,  are  displaced 
in  phase,  and  this  phase  dis- 
placement may  be  measured 
in  degrees  by  determining 
the  difference  in  the  degrees 
represented  by  the  two 
points  where  the  curves 
cross  the  horizontal  line 

(AB).  The  total  length  of  the  line  (AB)  corresponds  to  360 
degrees,  and  if  the  distance  between  the  two  points  where 
the  curves  (E)  and  (I)  cross  the  horizontal  line  is  %  of  the 
length  of  the  line  (AB),  the  e.m.f.  and  current  represented  by 
these  two  curves  are  displaced  in  phase  by  %  of  360  degrees, 
or  45  degrees.  The  current  lags  the  e.m.f.,  because  the  current 
curve  is  shown  as  crossing  the  horizontal  line  (AB),  as  you 
pass  along  the  line  from  left  to  right,  after  the  e.m.f.  curve. 
This  phase  displacement  may  be  expressed  in  time  as  well 
as  degrees.  Thus  the  time  interval  between  when  the  current 
and  e.m.f.  are  zero,  as  shown  in  Fig.  272,  is  %  of  a  period  or 
(1  -f-  8  X  frequency)  of  a  second.  The  displacement  in  prac- 
tice is  usually  measured  in  degrees  rather  than  time. 

372.  Chemical  and  Heating  Effects  of  an  Alternating  Cur- 
rent.— It  was  mentioned  in  Chapter  VIII  that  the  chemical 
effect  of  an  alternating  current  was  zero.  This  is  due  to  the 
fact  that  the  current  exists  in  the  circuit  in  one  direction  for 
the  same  time  that  it  exists  in  the  opposite  direction  and  as  a 
result  of  this  reversal  in  direction  there  will  be  a  chemical 
action  taking  place  first  in  one  direction  and  then  in  the 
opposite  direction,  and  the  resultant  chemical  action  will  be 
zero. 

The  power  expended  in  heating  a  conductor  at  any  instant 
is  equal  to  the  product  of  the  resistance  of  the  conductor  and 


THE  ALTERNATING-CURRENT  CIRCUIT 


335 


the  square  of  the  current  in  the  conductor.  In  an  alternating- 
current  circuit  the  current  is  constantly  changing  in  value 
and,  as  a  result,  the  power  expended  in  heating  the  conductors 
is  changing  in  value,  it  at  any  instant  being  equal  to  the 
product  of  the  resistance  and  the  square  of  the  current  at 
that  particular  instant.  In  order  to  obtain  the  total  heating 
effect  of  an  alternating  current,  it  is  necessary  to  add  up  all 
of  the  instantaneous  heating  effects.  The  heating  effect  of 
a  current  is  independent  of  the  direction  of  the  current  in  the 
circuit. 

373.  Sine  Wave  E.M.F.  or  Current. — If  a  simple  loop  of 
wire  be  revolved  at  a  constant  rate  in  a  uniform  magnetic 
field,  there  will  be  an  induced  e.m.f  set  up  in  the  coil,  which 
will  reverse  in  direction  and  change  in  value  as  the  coil 
rotates.  The  value  of  the  induced  e.m.f.  will  vary  as  the 
direction  of  motion  of  the  coil  changes  with  respect  to  the 
magnetic  field,  it  being  a  maximum  when  the  two  sides  of 
the  loop  move  perpendicular  to  the  magnetic  field  and  zero 
when  the  two  sides  of  the  loop  move  parallel  to  the  magnetic 


, 

^ 

^ 

•, 

/ 

:\ 

\ 

f 

1 

3 

\ 

\ 

-- 

^ 

r 

H 

\ 

\ 

/ 

\ 
\ 

$ 

/ 

/ 

/ 

N>  \ 

\ 

* 

/ 
NI 

A 

c 

\ 

/ 

3< 

^  i 

^ 

"y 

*-w    - 
3° 

s 

0° 

1 

50* 

Sv 
1 

\A 

70* 

Fig.  273 

field.  The  e.m.f.  induced  in  the  coil  for  positions  between 
those  just  mentioned  will  bear  a  definite  relation  to  the 
maximum  e.m.f.,  and  this  relation  can  be  determined  as  fol- 
lows: The  rate  at  which  the  two  sides  of  the  loop  are  mov- 
ing perpendicular  to  the  field  decreases  in  value  from  a  ver- 
tical position  and  becomes  zero  for  a  horizontal  position  of 
the  coil  when  the  field  is  vertical,  as  shown  in  Fig.  273.  The 
movement  of  the  coil  at  any  instant  can  be  resolved  into 
two  parts,  one  parallel  to  the  magnetic  field  and  the  other 
perpendicular  to  the  magnetic  field.  It  is  the  part  that  is  per- 


336 


PRACTICAL  APPLIED  ELECTRICITY 


pendicular  to  the  magnetic  field  that  results  in  an  e.m.f.  being 
induced  in  the  coil,  and  this  part  is  proportional  to  the  sine  of 
the  angle  the  path  of  the  two  sides  of  the  coil  make  with  the 
magnetic  field.  The  sine  of  this  angle  will  vary  as  the  pro- 
jection of  the  coil  on  the  vertical  plane.  If  the  projection 
when  the  coil  is  in  a  perpendicular  position  be  taken  as  rep- 
resenting the  maximum  e.m.f.,  the  e.m.f.  for  other  positions 
will  correspond  to  the  projection  of  the  coil  upon  the  vertical 
plane  for  those  positions.  Let  a  complete  revolution  be  rep- 
resented by  the  horizontal  line  (AB),  it  corresponding  to  360 

degrees,  then  the  relation 
of  the  e.m.f.'s  for  various 
angular  positions  can  be 
laid  off  on  ordinates  drawn 
vertically  through  points 
on  the  line  (AB),  which 
correspond  to  the  angular 
displacement  of  the  coil 


360 


from  a  position  perpendic- 
ular to  the  field.  The  values 
for  the  45°  positions  are  the 
only  ones  shown  in  the  fig- 
ure; the  remaining  ones, 
however,  are  determined 
in  the  same  way.  Such  a 
curve  is  called  a  sine 

curve,  since  its  ordinates  vary  as  the  sine  of  the  angle  rep- 
resented by  the  point  on  the  line  (AB)  through  which  the 
ordinate  passes.  An  e.m.f.  or  current  whose  value  varies  as 
the  ordinate  of  a  sine  curve  is  called  a  sine  e.m.f.  or  current. 
The  following  calculations  are  all  based  on  a  sine  curve.  The 
e.m.f.  and  current  curves  met  with  in  practice  are  very  sel- 
dom sine  curves,  but  approach  a  sine  curve  quite  often. 

374.  Maximum,  Average,  and  Effective  Values  of  E.M.F. 
and  Current. — The  maximum  value  of  an  alternating  e.m.f.  or 
current  is  the  value  represented  by  the  ordinate  of  the  e.m.f. 
or  current  curve  having  the  greatest  length.  Thus  in  Fig. 
274  the  maximum  e.m.f.  occurs  at  90°  and  270°,  it  being  op- 
posite in  direction  for  the  two  positions  but  having  the  same 
value. 

The  average  value   of  an   alternating  e.m.f.   or  current  is 


THE  ALTERNATING-CURRENT  CIRCUIT  337 

equal  to  the  average  of  all  of  the  instantaneous  e.m.f.'s  or 
currents  for  a  complete  alternation,  starting  with  zero  value 
and  returning  to  zero  value.  For  a  true  sine  wave  the  aver- 
age e.m.f.  and  current  are  always  .636  times  their  maximum 
value.  This  relation  is  determined  by  finding  the  area  of  a 
positive  or  negative  loop  of  the  e.m.f.  or  current  curve  and 
dividing  this  area  by  the  distance  between  the  two  points 
where  the  curve  crosses  the  horizontal  line.  The  rectangles, 
shown  by  the  shaded  portions  in  Fig.  274,  have  each  the  same 
area  as  one  loop  of  the  sine  curve,  and  the  altitude  of  this 
rectangle  is  .636  times  the  maximum  ordinate  of  the  sine 
curve. 

The  effective  value  of  an  alternating  current  is  numerically 
equal  to  a  steady  direct  current  that  will  produce  the  same 
heating  effect  in  a  given  time  as  is  produced  by  the  changing 
alternating  current.  If  a  conductor  has  a  resistance  of  (R) 
ohms  and  there  is  an  alternating  current  in  the  conductor, 
the  power  expended  in  heating  the  conductor  at  any  instant 
is  equal  to  the  value  of  the  current  at  that  instant  squared, 
times  the  resistance  in  which  the  current  exists.  Adding  up 
all  of  these  instantaneous  heating  effects  for  a  certain  time 
gives  the  total  heating  effect.  This  resultant  or  total  heating 
effect  could  be  produced  by  a  steady  direct  current  as  well 
as  by  an  alternating  current.  Now  the  value  of  the  steady 
direct  current  required  to  produce  the  same  heating  effect  as 
is  produced  by  the  alternating  current  corresponds  in  value 
to  the  effective  alternating  current 

I2R  =  average  i2R, 
or 

12  =  average  i2 
and 


I  =  V  average  i2 

Note — Small   letters   are   used   to   represent   instantaneous 
values. 

For  a  sine  wave  the  square  root  of  the  average  of  the  in- 
stantaneous values  squared  is  equal  to  .707  times  the  max- 
imum current. 

Average  value  =  .636  maximum  value 
Effective  value  =  .707  maximum  value 
Effective  value  =  1.11  average  value 


338 


PRACTICAL  APPLIED  ELECTRICITY 


The  effective  value  divided  by  the  average  value  is  equal  to 
1.11,  which  is  called  the  form  factor  of  the  wave.  The  above 
relations  hold  true  for  sine  waves  only. 


Fig.  275 


Fig.  276 


375.  Vector    Representation    of    Alternating    E.M.F.'s    and 
Currents. — A  vector  quantity  is  one  having  both  direction  and 
magnitude;     it    may    be    represented    by    a    line,    called    a 
vector,   drawn   in   a   definite   direction   corresponding   to   the 
direction  of  the  quantity  it  represents  and  having  a  length 
corresponding  to  the  value  of  the  vector  quantity  to  a  suitable 
scale.    Thus  a  current  of  10  amperes  and  an  e.m.f.  of  10  volts, 
displaced  in  phase  by  30  degrees,  would  be  represented  as 
shown  in  Fig.  275. 

These  vectors  can  be  thought  of  as  rotating,  and  one 
revolution  corresponds  to  360  degrees.  The  counter-clockwise 
direction  of  rotation  is  taken  as  positive.  In  representing 
alternating  e.m.f.'s  and  current  by  vectors,  the  effective  values 
are  the  ones  usually  used. 

376.  Addition  and  Subtraction  of  Vectors. — Two  vectors  are 
added  in  the  same  way  as  two  forces  are  added  in  determining 
the  resultant  force.   The  two  vectors  (E^  and  (E2),  shown  in 
Fig.  276,  are  added  by  completing  the  parallelogram,  as  shown 
by  the  dotted  lines,  and  drawing  the  diagonal  gives  the  re- 
sultant (E).    Its  direction  is  that  indicated  by  the  arrowhead. 

Two  vectors  are  subtracted  by  reversing  one  and  adding 
them.  Thus  if  it  is  desired  to  know  the  value  of  (El  —  E2), 
shown  in  Fig.  276,  the  vector  (E2)  is  reversed  in  direction  and 
then  added  to  the  vector  (E^) ;  the  direction  of  the  vector 
(E),  representing  the  difference,  is  shown  in  the  figure  by  the 
arrow  head. 

377.  Factors  Determining  the  Value  of  an  Alternating  Cur- 
rent.— The  current  in  a  circuit  upon  which  there  is  a  steady 


THE  ALTERNATING-CURRENT  CIRCUIT 


339 


direct  voltage  impressed  is  equal  to  the  value  of  the  impressed 
voltage  in  volts  divided  by  the  total  resistance  in  ohms.  In 
an  alternating-current  circuit  upon  which  there  is  a  constant 
effective  pressure  impressed,  the  value  of  the  effective  current 
is  determined  not  by  the  resistance  alone  but  by  the  combined 
effects  of  the  resistance,  inductance,  and  capacity,  if  they  all 
be  present  in  the  circuit.  If  there  is  no  inductance  or  capacity 
in  the  circuit,  then  the  same  law  holds  for  the  alternating- 
current  circuit  as  is  true  for  the  direct-current  circuit.  The 
current  in  the  alternating-current  circuit  will  be  equal  to  the 
impressed  voltage  divided  by  the  resistance  of  the  circuit 


Fig.  277 


0°       -UO 


when  the  effects  of  the  inductance  and  capacity  are  exactly 
equal,  they  acting  in  opposition  to  each  other,  as  will  be 
explained  later. 

378.  E.M.F.'s  Required  to  Overcome  K:sistance. — The  e.m.f. 
at  any  instant  required  to  overcome  the  resistance  of  a  circuit 
is  equal  to   the  product  of  the  current  at  that  instant  and 
the  resistance  of  the  circuit,  or  (IR).    If  there  be  an  alternat- 
ing current,  as  represented  by  the  curve  (I)  in  Fig.  278,  in  a 
circuit,  the  e.m.f.  at  any  instant  required  to  produce  this  cur- 
rent is  equal  to    (IR)   and  varies  directly  as  the  current  or 
passes  through  corresponding  values  at  the  same  time.     The 
current  and  e.m.f.  will,  as  a  result,  be  in  phase,  and  the  curve 
(Er)  represents  the  impressed  e.m.f.  required  to  produce  the 
current  (I). 

379.  Hydraulic  Analogy  of  Inductance. — If  the  electric  cur- 
rent in  an  alternating-current  circuit  be  represented  by  a  fluid 
that  flows  through  a  pipe,  as  shown  in  Fig.  279,  due  to  the 


340 


PRACTICAL  APPLIED  ELECTRICITY 


M 


alternating  pressure  that  is  created  by  the  pump  (P),  then  an 
inductance  in  such  a  circuit  can  be  represented  by  a  fluid 
motor  (M)  similar  to  that  shown  in  the  figure.  When  such 

a  motor  is  connected  in 
the  circuit,  considerable 
time  will  be  required  for 
the  current  of  liquid  to 
reach  a  maximum  steady 
value  if  a  constant  pres- 
sure be  applied  to  the  cir- 
cuit by  the  pump,  on  ac- 
count of  the  inertia  of  the 
wheel  (W)  that  is  attached 
to  the  fluid  motor.  Alter 
the  pressure  has  been  ap- 
plied to  the  motor  for  some 
time,  the  motor  will  have 

reached  a  speed  such  that  it  offers  practically  no  resistance 
to  the  flow  of  the  liquid  through  it.  If,  however,  there  be  a 
change  in  the  pressure  produced  by  the  pump,  there  will  be 
a  tendency  for  the  current  of  liquid  to  change  in  value,  and 
the  action  of  the  fluid  motor  will  always  be  such  as  to  tend 
to  prevent  a  change  in  the 
current — that  is,  if  the  cur- 
rent tends  to  increase  in 
value  due  to  an  increase  in 
pump  pressure,  the  motor 
will  oppose  this  increase, 
and  if  the  current  tends  to 
decrease  in  value,  due  to  a 
decrease  in  pump  pressure, 
the  motor  will  tend  to  pre- 


Fig.  279 


360 


vent  this  decrease.    The  ac- 
tion of  the  motor  at  all  times 

is  such  as  to  tend  to  prevent  any  change  in  the  value  of  the 
current  in  the  circuit  of  which  it  is  a  part. 

The  motor  in  the  hydraulic  problem  just  discussed  corre- 
sponds in  action  to  the  inductance  of  an  alternating-current 
circuit  in  which  there  is  an  alternating  current.  In  the 
hydraulic  problem,  if  an  alternating  pressure  be  applied  to  the 
motor  instead  of  a  direct  pressure,  its  direction  of  rotation 


THE  ALTERNATING-CUEEENT  CIRCUIT  341 

will  change  twice  per  cycle  of  the  impressed  pressure.  The 
direction  of  rotation,  however,  will  not  change  at  the  same 
instant  the  pressure  produced  by  the  pump  changes  on  ac- 
count of  the  inertia  possessed  by  the  moving  parts  of  the 
fluid  motor.  The  motor  will  continue  to  rotate  in  a  given 
direction  for  some  time  after  the  pressure  has  been  reversed 
in  direction.  The  velocity  of  the  paddle  wheel  of  the  motor 
determines  the  value  of  the  current  of  liquid  through  it,  and 
the  direction  of  rotation  of  the  paddle  wheel  determines  the 
direction  of  the  current.  Since  the  velocity  of  the  fluid  motor 
is  not  a  maximum  when  the  pressure  of  the  pump  is  a  max- 
imum, it  reaching  a  maximum  velocity  in  a  given  direction 
after  the  pressure  produced  by  the  pump  has  reached  its 
maximum  value  in  the  same  direction,  and  the  velocity  of  the 
motor  is  zero  after  the  pressure  of  the  pump  is  zero,  the  cur- 
rent of  liquid  in  the  circuit  must  lag  the  pressure. 

380.  Phase  Relation  of  E.M.F.  to  Overcome  Inductance  and 
the  Current  in  an  Alternating-Current  Circuit. — Assume  there 
is  a  circuit  containing  inductance  alone,  and  that  there 
is  a  current  in  this  circuit  represented  by  the  curve  (I), 
Fig.  280.  The  magnetic  field  created  by  the  current  at  any 
time  will  depend  upon  its  instantaneous  value.  Thus  the 
magnetic  field  or  lines  of  force  associated  with  the  current 
will  be  a  maximum  when  the  current  is  a  maximum,  will  de- 
crease or  increase  in  value  with  a  decrease  or  increase  in  the 
value  of  the  current,  and  will  reverse  in  direction  at  the  same 
time  the  current  reverses  in  direction.  Since  the  above  rela- 
tion exists  between  the  current  in  the  circuit  and  the  magnetic 
flux  produced  by  the  current,  a  second  curve  ($)  may  be 
drawn,  as  shown  in  Fig.  280,  whose  ordinate  at  any  instant  will 
represent  to  a  suitable  scale  the  magnetic  flux  at  that  instant. 
With  a  change  in  the  magnetic  flux  associated  with  the  cir- 
cuit, there  will  be  an  induced  e.m.f.  set  up  in  the  circuit, 
which  at  any  instant  is  proportional  to  the  rate  at  which  the 
flux  is  changing  with  respect  to  the  circuit,  or  the  rate  at 
which  the  conductor  forming  the  circuit  is  cutting  the  lines  of 
force.  By  investigating  curve  (3>)  it  is  seen  that  the  flux  is 
changing  at  its  greatest  rate  when  it  is  zero  in  value  and  is 
changing  at  a  minimum  rate  when  it  is  at  its  maximum  value; 
or  the  induced  e.m.f.  in  the  circuit  is  zero  at  the  points  (C) 
and  (E)  and  is  a  maximum  at  the  points  (A),  (D),  and  (B). 


342 


PRACTICAL  APPLIED  ELECTRICITY 


The  value  of  the  induced  e.m.f.  at  any  other  time  during  the 
cycle  will  depend  upon  the  rate  at  which  the  flux  is  changing 
in  value,  and  its  direction  will,  according  to  Lenz's  Law,  al- 
ways be  such  as  to  oppose  a  change  in  the  value  of  the  current 
in  the  circuit.  Thus,  if  the  current  be  increasing  in  value  in 
the  positive  direction,  as  it  is  between  the  points  (A)  and  (C), 
the  induced  e.m.f.  acts  in  such  a  direction  as  to  oppose  this 
change  in  the  current,  or  it  acts  in  the  negative  direction.  If 
the  current  be  decreasing  in  value  in  the  positive  direction, 
the  induced  e.m.f.  opposes  this  decrease,  or  it  acts  in  the 
positive  direction..  The  curve  (ei)  represents  the  e.m.f. 
induced  in  the  circuit.  If  the  circuit  has  no  resistance  (a 
theoretical  condition),  the  only  e.m.f.  required  to  produce  the 
current  (I)  in  the  circuit  would  be  one  that  would  overcome 
the  e.m.f.  (ei).  Such  an  e.m.f.  would  be  represented  by  the 
curve  (Ei),  whose  ordinates  are  at  each  instant  equal  to 
those  of  (ei)  but  opposite  in  sign,  or  (Ei)  acts  opposite  to 
(ei),  and  will  produce  the  current  (I).  From  the  relation 
of  the  curve  (I)  and  (Ei)  in  the  figure,  it  is  seen  that  the 
current  and  impressed  e.m.f.  in  an  inductive  circuit  are  dis- 
placed in  phase  by  90°  and  that  the  current  lags  the  e.m.f. 

381.  Hydraulic  Analogy 
of  Capacity. — The  hydraul- 
ic analogy  of  a  condenser 
is  shown  in  Fig.  281.  A 
flexible  rubber  diaphragm 
(D)  is  stretched  across  a 
specially  constructed 
chamber  (C)  which  is  con- 
nected to  a  pump  (P),  as 
shown  in  the  figure,  that 
produces  an  alternating 
pressure.  When  the  dia- 
phragm (D)  is  in  its  nor- 
mal position,  it  offers  no  opposition  to  the  flow  of  the 
liquid  through  the  pipe  in  either  direction.  As  soon,  how- 
ever, as  the  diaphragm  is  displaced  from  its  neutral  posi- 
tion, it  sets  up  a  reaction  which  opposes  the  flow  of  the 
liquid,  and  this  reaction  will  increase  in  value  as  the  dia- 
phragm is  displaced  more  and  more,  finally  reaching  a  value 
equal  to  the  pressure,  causing  the  liquid  to  flow  through 


Fig.  281 


THE  ALTEENATING-CUKEENT  CIRCUIT 


343 


the  pipe,  and  when  the  reaction  becomes  equal  to  the  acting 
pressure  there  will  be  no  current.  If,  now,  the  current  be  re- 
versed in  direction,  the  diaphragm  will  return  to  its  normal 
position,  and  while  it  is  returning,  it  will  act 'in  the  same 
direction  as  the  current.  When  the  diaphragm  has  reached 
its  normal  position  and  it  is  forced  to  the  opposite  side,  it 
will  immediately  react  upon  the  current  and  tend  to  stop  it, 
and  this  reaction  will  finally  reach  such  a  value  that  there 
will  be  no  current  in  the  circuit.  It  is  seen,  then,  that  the 
diaphragm  acts  with  the  current  one-half  of  the  time  and  in 
opposition  to  it  one-half  of  the  time.  The  reaction  of  the 
diaphragm  corresponds  to  the  electrical  pressure  at  the 
terminals  of  a  condenser  connected  in  an  alternating-current 
circuit,  and  it  has  a  maximum  value  when  the  current  is  zero 
and  a  zero  value  when  the  current  is  a  maximum. 

382.  Phase  Relation  of  the  E.M.F.  to  Overcome  the  Effect 
of  Capacity  and  the  Current  in  an  Alternating-Current  Circuit. 
— The  current  in  a  circuit  containing  capacity  alone  may  be 
represented  by  a  curve  such  as  (I),  Fig.  282.  The  flow  of 
liquid  through  the  chamber  (C),  Fig.  281,  could  be  repre- 
sented by  such  a  curve,  and 
since  the  reaction  of  the 
diaphragm  corresponds  to 
the  e.m.f.  at  the  terminals 
of  the  condenser,  the  phase 
relation  of  the  e.m.f.  and 
the  current  can  be  deter- 
mined by  an  investigation 
of  Fig.  281,  carrying  the  op- 
eration through  a  complete 

cycle.  The  position  of  the  diaphragm  must  be  normal 
when  the  current  is  a  maximum,  say  at  the  point  (C), 
Fig.  282,  as  it  produces  no  opposition  to  the  flow  of 
liquid.  As  the  diaphragm  is  extended  to  either  side,  its 
reaction  increases  and  it  opposes  the  flow  of  liquid,  or  if 
the  current  is  in  the  positive  direction,  the  action  of  the 
diaphragm  is  negative.  If  the  current  reverses  in  direction 
when  it  has  reached  a  zero  value  and  starts  to  increase  in 
value  in  the  negative  direction,  the  diaphragm  will  act  with 
the  current  or  they  will  both  be  negative.  When  the  di- 
aphragm has  reached  its  normal  position,  its  reaction  is  zero 


180"        270° 
Fig.  282 


360 


344  PRACTICAL  APPLIED  ELECTRICITY 

and  the  current  is  a  maximum,  and  at  this  point  the  reaction 
of  the  diaphragm  changes  sign  and  the  current  starts  to 
decrease  in  value  in  the  negative  direction.  While  the  cur- 
rent is  decreasing  in  value  in  the  negative  direction,  the  reac- 
tion of  the  diaphragm  is  increasing  in  value  in  the  positive 
direction.  The  current  again  reverses  in  direction  after  reach- 
ing zero  value  and  starts  to  increase  in  the  positive  direction, 
the  reaction  of  the  diaphragm  decreasing  in  value  in  the  posi- 
tive direction,  which  completes  the  cycle.  The  curve  (ec), 
Fig.  282,  represents  the  reaction  of  the  diaphragm,  or  the 
electrical  pressure  at  the  terminals  of  a  condenser  connected 
in  an  alternating-current  circuit  carrying  a  current  (I).  Since 
the  curve  (ec)  represents  the  reaction  in  the  circuit,  the  e.m.f. 
required  to  overcome  this  reaction  must  be  equal  in  value  and 
opposite  in  direction  to  it  at  each  instant.  The  curve  (Ec) 
then  represents  the  e.m.f.  required  to  overcome  the  effect  of 
the  capacity  in  a  circuit  and  produce  the  current  (I).  It  is 
seen  by  an  inspection  of  the  curves  that  the  current  (I)  leads 
the  impressed  e.m.f.  (Ec)  by  90  degrees. 

383.  E.M.F.  Required  to  Overcome  Combined  Effects  of 
Resistance,  Inductance,  and  Capacity. — By  comparing  the 
curves  (Ei)  and  (Ec)  in  Figs.  280  and  282,  it  is  seen  that 
they  are  displaced  in  phase  by  180  degrees,  or  the  e.m.f.'s  they 
represent  act  just  opposite  to  each  other.  If  now  inductance 
and  capacity  be  present  in  a  circuit  at  the  same  time,  the 
electrical  pressures  required  to  overcome  their  effects  would 
tend  to  neutralize.  When  the  effects  of  inductance  and 
capacity  are  equal,  the  two  e.m.f.'s  exactly  neutralize,  and  the 
only  e.m.f.  required  would  be  that  to  overcome  the  resistance 
of  the  circuit.  The  current  and  impressed  e.m.f.  in  such  a 
circuit  would  be  in  phase.  If,  however,  the  e.m.f.'s  required 
to  overcome  the  effects  of  inductance  and  capacity  are  not 
equal,  they  will  not  exactly  neutralize  and  there  will  be  a 
resultant  e.m.f.  in  the  circuit  to  overcome,  which  has  a  value 
at  any  instant  equal  to  the  difference  between  the  e.m.f.'s  to 
overcome  the  effects  of  inductance  and  capacity.  The  e.m.f.'s 
required  to  overcome  the  effects  of  resistance,  inductance,  and 
capacity,  and  thus  produce  the  current  (I),  are  shown  in 
Fig.  283.  The  e.m.f.  required  to  overcome  the  effect  of  in- 
ductance in  this  case  is  greater  than  that  required  to  overcome 
the  effect  of  capacity,  and  they  will  not  exactly  neutralize 


THE  ALTERNATING-CURRENT  CIKCUIT 


345 


90  180" 

Fig.  283 


£70        360 


each  other.  The  curve  (R)  represents  their  combined  value. 
This  resultant  pressure  represented  by  the  curve  (R)  must 
now  be  combined  with  the  e.m.f.  to  overcome  the  resistance 
(Er)  in  order  to  obtain  the  impressed  pressure  required  to 
produce  the  current  (I).  These  two  curves  can  be  combined 
by  adding  their  ordinates  for 
various  points  along  the  hori- 
zontal line  (AB),the  algebraic 
sum  of  their  ordinates  at  any 
point  being  the  ordinate  of 
the  resultant  curve  (E),  which 
represents  the  total  pressure 
that  must  be  impressed  upon 
the  circuit  to  produce  the  cur- 
rent (I).  When  the  pressure 
required  to  overcome  the  ef- 
fect of  the  inductance  is  o* 
greater  than  the  pressure  re- 
quired to  overcome  the  effect 

of  the  capacity,  the  current  lags  the  impressed  pressure,  as 
shown  in  Fig.  283.  If  the  pressure  required  to  overcome  the 
effect  of  the  capacity  is  greater  than  that  to  overcome  the 
effect  of  the  inductance,  the  current  in  the  circuit  will  lead 
the  impressed  pressure. 

384.  Numerical  Values  of  E.M.F.  Required  to  Overcome 
Resistance,  Inductance,  and  Capacity. — If  the  current  in  a  cir- 
cuit changes  in  value  according  to  the  sine  law,  and  (I)  be 
taken  as  the  effective  value  of  the  current  in  the  circuit,  the 
pressures  required  to  overcome  the  effect  of  the  inductance 
and  capacity  can  be  determined  by  means  of  the  equations 

Ei=2X7rXfXLXl  (131) 

I 

Ec  = (132) 

2  X  TT  X  f  X  C 

In  the  above  equations  (f )  represents  the  frequency  in  cycles 
per  second,  TT  =  3.1416,  (L)  is  the  inductance  of  the  circuit  in1 
henrys,  (C)  is  the  capacity  in  farads,  and  (I)  is  the  effective 
current  in  amperes.  (Ei)  and  (Ec)  represent  the  effective 
e.m.f.'s  required  to  overcome  the  effects  of  the  inductance 
and  capacity,  respectively.  The  e.m.f.  required  to  overcome 
the  effect  of  inductance  leads  the  current  by  90  degrees,  and 


346  PRACTICAL  APPLIED  ELECTRICITY 

the  e.m.f.  required  to  overcome  the  effect  of  capacity  lags  the 
current  by  90  degrees.  The  e.m.f.  required  to  overcome  the 
resistance  is  equal  to  (RI)  and  it  is  always  in  phase  with  the 
current.  These  three  e.m.f.'s  can  be  represented  by  three 
vectors,  as  shown  in  Fig.  284,  the  counter-clockwise  direction 
of  rotation  being  taken  as  positive. 

385.      Total    Electromotive    Force    Required    to    Produce    a 
Given  Alternating  Current.— If  the  two  quantities  (2  X  TT  X  f  X 
L  X  I)  and  (I-f-2X7rXfXC),  Fig.  284,  are  equal  in  value, 
the  vectors  representing  them  will  be 
equal  in  length.  The  resultant  of  these 

2TrfLIk^\  NJ^*  two  vectors  then  will  be  zero,  and  the 
v£  only  e.m.f.  required  to  produce  the 
*°  current  (I)  is  that  to  overcome  the  re- 

»     sistance,  which  is  equal  to  (RI). 

If,   however,   the   e.m.f.   required  to 
50°  overcome  the  effect  of  the  inductance 

2frfr  *  is  greater  than  that  to  overcome  the 

capacity,  the  vector  (Ei),  Fig.  285,  will 
Fig.  284  be  greater  in  length  than  the  vector 

(Ec).     The    resultant    of    these    two 

e.m.f.'s  will  be  equal  to  (Ei — Ec),  and  its  direction  will  corre- 
spond to  that  of  the  larger  vector,  or  (Bi).  This  resultant 
must  now  be  combined  with  (E,-)  in  order  to  obtain  the  total 
e.m.f.  required  to  produce  the  current  (I),  which  can  be  done 
graphically,  as  shown  in  the  figure.  The  resultant  (E)  is 
equal  to  the  diagonal  of  a  parallelogram  whose  sides  are 
(Ei — Ec)  and  (Er),  and  its  value  is  equal  to  the  square  root  of 
the  sum  of  the  squares  of  the  two  sides,  or 


E=  V  E2  +  (Et  — Ec)2  (133) 

Substituting  in  the  above  equation  the  values  of  (Ei)  and 
(Ec)  as  given  in  equations  (131)  and  (132),  and  the  value 
of  (Er),  which  is  equal  to  (RI),  gives  the  equation 


-V 


E  =        (RI)2+       27rfLI (134) 

27TfC    * 

By  taking  (I)  from  under  the  radical  sign,  this  equation  can 
be  changed  to  the  form 


THE  ALTERNATING-CURRENT  CIRCUIT 


347 


R2 


—  -\ 

7TfC' 


or 


E 


1  = 


(135) 


(136) 


2  7T  f  L 

2     TTfC 

The  above  equation  gives  the  value  of 
the  current  (I)  in  terms  of  the  im- 
pressed electromotive  force  (E),  the 
ohmic  resistance  of  the  circuit  (R), 
the  inductance  (L)  in  henrys,  the 
capacity  (C)  in  farads,  frequency  (f) 
in  cycles  per  second,  and  the  constant 
(27r),  which  is  equal  to  (2  X  3.1416) 
or  6.2832. 

386.  Impedance  and  Reactance  of  a 
Circuit. — The  impedance  of  a  circuit  in 
which  there  is  an  alternating  current  is 

the  total  opposition  offered  by  the  circuit  to  the  flow  of  the 
electricity  through  it.  The  letter  (Z)  is  usually  used  to  'rep- 
resent the  impedance.  It  is,  from  equation  (136),  numerically 
equal  to 


Fig.  285 


->! 


=          R2 


27Tf    L  — 


(137) 


27rf  C  ' 

The  impedance  of  a  circuit  is  composed  of  two  factors,  the 
resistance  and  the  reactance.  The  reactance  is  the  quantity 
which,  when  multiplied  ,by  the  current,  gives  the  component 
of  the  impressed  e.m.f.  that  is  at  right  angles  to  the  current. 
The  resistance  multiplied  by  the  current  gives  the  component 
of  the  impressed  e.m.f.  in  phase  with  the  current.  The  re- 
actance, which  is  usually  represented  by  the  letter  (X),  is 
equal  to 


L  — 


(138) 


27Tf     C 

The  above  value  of  (X)  is  composed  of  two  factors,  (27rfL)  and 
(l~27rfC).  The  quantity  (27rfL)  is  called  the  inductance  re- 
actance and  is  represented  by  the  symbol  (Xi),  while  the 


348 


PRACTICAL  APPLIED  ELECTRICITY 


quantity  (1  -5-  2?rfc)  is  called  the  capacity  reactance  and  is 
represented  by  the  symbol  (Xc).  In  general: 

Z=VR2  +  X2  (139) 

or 

Z  =  VR2+  (X,— Xc)2  (140) 

The  inductance  reactance  (Xi)  is  considered  as  positive  and 
the  capacity  reactance  (Xc)  as  negative,  when  they  are  being 
combined.  The  impedance  and  the  reactance  of  a  circuit  are 
measured  in  ohms  just  as  the  resistance  is  measured  in  ohms. 

387.     Impedance     Diagram. — Since 
the  impedance  of  a  circuit  is  equal 
to  the  square  root  of  the  sum  of  the 
X=(Xl~X(0      squares  of  two  quantities,   as   given 
in  equation    (139),  a  right-angle  tri- 
R  angle    can   be   drawn,    as    shown   in 

Fig.  286  Fig.  286,  its  three  sides  representing 

the  resistance,  reactance,  and  im- 
pedance. Such  a  figure  is  called  an  impedance  diagram. 
388.  Impedances  in  Series. — Any  number  of  impedances  in 
series  can  be  added  by  adding  their  resistances  and  reactances, 
respectively,  which  gives  the  resistance  and  the  reactance  of 
the  resultant  impedance.  Thus  two  impedances,  (Zx)  and 
(Z2)  connected  in  series,  may  be  added  as  shown  in  Fig.  287a, 
both  reactances  being  positive.  If  one  of  the  reactances  be 
negative,  the  impedances  are  added  as  shown  in  Fig.  287b, 


r — (R.+R 


Fig.  287  a 


Fig.  287  b 


the  resultant  reactance  being  negative;  it  may,  however, 
be  positive,  depending  upon  whether  the  negative  react- 
ance is  greater  or  less  than  the  positive  reactance.  If  the 
resultant  reactance  is  positive,  the  current  lags  thee.m.f.;  and 


THE  ALTERNATING-CURRENT  CIKCUIT  349 

if  the  resultant  reactance  is  negative,  the  current  leads  the 
e.m.f.     The  impedance  of  a  series  circuit  composed  of  a  num- 
ber of  impedances  (Zx),  (Z2),(Z3),  etc.,  can  be  calculated  by 
substituting  in  the  following  general  equation 
Z  =  V  (Ri  +  R2  +  R3  +  etc.) a  +  (Xx  +  X2  +  X3  +  etc.)2    (141) 

Example. — Calculate  the  total  impedance  of  a  circuit  com- 
posed of  two  impedances  in  series  having  resistances  of  10  and 
5  ohms  and  reactances  of  15  and  — 5  ohms,  respectively. 

Solution.— The  total  resistance  of  the  circuit  is  (10  +  5),  or 
15  ohms  and  the  resultant  reactance  is  [15+  ( — 5)],  or  10 
ohms.  Combining  the  total  resistance  and  the  resultant 
reactance  gives 


Z  =  V  (15)2+  (10)2=  18.03— 

Ans.     18.03 —  ohms. 

389.  Impedances  in  Parallel. — In  calculating  the  combined 
impedance  of  a  number  of  impedances  in  parallel,  an  equation 
is  used  similar  to  equation  (141),  but  instead  of  using  the 
separate  resistances  and  reactances,  the  conductance  and  sus- 
ceptance  of  the  circuit  are  used. 

The  conductance  of  a  circuit  is  the  quantity  by  which  the 
e.m.f.  must  be  multiplied  to  give  the  component  of  the  current 
parallel  to  the  e.m.f. 

The  susceptance  of  a  circuit  is  the  quantity  by  which  the 
e.m.f.  must  be  multiplied  to  give  the  component  of  the  cur- 
rent perpendicular  to  the  e.m.f. 

Admittance,  conductance,  and  susceptance  are  all  measured 
in  a  unit  called  the  mho. 

The  conductance  is  represented  by  the  letter  (G)  and  it  is 
numerically  equal  to 

R  R 

G  = =  —  (142) 

R2  +  X2         Z2 

The  susceptance  is  represented  by  the  letter   (B)   and  it  is 
numerically  equal  to, 

X  X 

B=—  (143) 

R2  +  X2       Z2 

The  reciprocal  of  the  impedance  of  a  circuit  is  called  the 
admittance  and  is  represented  by  the  letter  (Y). 


350  PRACTICAL  APPLIED  ELECTRICITY 

1 

Y=-  (144) 

Z 

Since 

E 
Z  =  -  (145) 

I 
Then 

Y  =  I-^E  (146) 

The  admittance  of  a  circuit  bears  the  same  relation  to  the 
conductance  and  susceptance  as  exists  between  the  impedance, 
resistance,  and  reactance,  or 


Y=  V  G2  +  B2  (147) 

The  total  impedance  of  a  number  of  devices  connected  in 
parallel  then  is  equal  to  the  reciprocal  of  the  admittance, 
which  can  be  determined  by  the  equation 


Y  =  V  (Gx  +  G2  +  etc.)>  +  (Bi  +  B2  +  etc.)2  (148) 

Example. — Calculate  the  total  impedance  of  two  impedances 
in  parallel  having  resistances  of  8  and  6  ohms,  and  reactances 
of  4  and  5  ohms,  respectively. 

Solution. — Substituting  in  equation  (142)  gives  the  value  of 
the  conductance  of  the  first  branch  (Gi),  equal  to 

8  81 

GI  =  —  —  =  .1  mho 

82  -f  42      80       10 

and  the  conductance  of  the  second  branch  (G2)  equal  to 

6  6 

G2  =  -  =  —  =  .983  mho 

62  4-  52      61 

Substituting  in  equation  (143)  gives  the  value  of  the  suscept- 
ance of  the  first  branch  (B^,  equal  to 

4  41 

B!  = =  —  =  —  =.05  mho 

82  +  42      80       20 

and  the  susceptance  of  the  second  branch  (B2),  equal  to 

5     5 

B2  =  —      —  =  —  =  .0819  mho 
62  +  52       61 

The  total  conductance  (G)  of  the  circuit  is  equal  to  (Gx  +  G2), 


THE  ALTERNATING-CURRENT  CIKCUIT 


351 


or 


G=.l  +  .0983  =  .1983 
susceptance    (B)    of   the   circuit   is    equal   to 


and   the   total 
(Bi  +  B2),  or 

B  =  .05  +  .0819  =  .1319 

The  admittance  may  now  be  obtained  by  substituting  in  equa 
tion  (147),  which  gives 

Y=  V  (.1983)2  +  (.1319)2 
=  V  .039  323  +  .017  398 


=  V  .056  72 
=  .238  mho 

The  impedance  is  equal  to  the  reciprocal  of  the  admittance,  or 

1 

Z  = =4.20 

.238 

Ans.  4.20  ohms. 

390.  Phase  Relation  of  the  Current  and  Potential  Drops  in 
a  Series  Circuit. — The  series  circuit  shown  in  Fig.  288  is  com- 
posed of  three  parts,  a  resistance  (R),  an  inductance  (L),  and 
a  condenser  (C).  The  current  is  the  same  in  all  parts  of  such 


Fig.  288 

a  circuit  and  an  ammeter,  that  will  operate  on  alternating 
current,  may  be  connected  in  the  circuit  at  any  point  and  it 
will  indicate  the  current  that  exists  in  the  circuit. 

A  voltmeter  (V)  may  be  connected  across  the  entire  circuit, 
as  shown  in  the  figure,  and  it  will  indicate  the  drop  in  poten- 
tial over  all  three  parts  of  the  circuit  combined.  Three  other 
voltmeters  (Vr),  (Vi),  and  (Vc),  may  be  connected  across 


352 


PRACTICAL  APPLIED  ELECTRICITY 


the  resistance,  inductance  and  capacity,  respectively,  as  shown 
in  the  figure,  and  their  indications  will  be  a  measure  of  the 
drop  in  potential  over  the  three  parts  of  the  circuit.  The  sum 
of  the  indications  of  the  three  voltmeters,  (Vr),  (Vi),  and 
(Vc),  will  be  greater  than  the  indications  of  the  voltmeter 
(V)  for  the  following  reason:  The  drop  in  potential  over  the 
resistance  is  in  phase  with  the  current,  the  drop  in  potential 
over  the  inductance  leads  the  current,  and  the  drop  in  potential 
over  the  capacity  lags  the  current.  Since  these  three  drops 
in  potential  are  not  in  phase,  their  resultant  is  not  equal  to 
their  numerical  sum.  The  drops  over  the  inductance  and 
capacity  may  neutralize  each  other,  being  opposite  in 
phase,  in  which  case  the  voltmeter  (Vr)  would  indicate  the 
same  drop  as  the  voltmeter  (V).  In 
an  alternating-current  circuit  the  sum 
of  the  drops  over  the  various  parts  of 
the  circuit  is  not  equal  to  the  im- 
pressed voltage  except  in  a  circuit  con- 
taining resistance  alone. 

391.  Phase  Relation  of  Currents  and 
Potential  Drops  in  a  Divided  Circuit. — 
A  divided  circuit  composed  of  three 
branches  is  shown  in  Fig.  289.  The 
upper  branch  is  a  non-inductive  resist- 
ance, the  middle  branch  is  an  induct- 
ance, and  the  lower  branch  is  a  ca- 
pacity. A  voltmeter  (V)  connected 
between  the  terminals  (D)  and  (B) 
indicates  the  drop  in  potential  over 
each  of  the  three  branches  of  the  di- 
vided circuit.  The  current  in  any  one 
of  the  branches  is  equal  to  the  indica- 
tion of  the  voltmeter  (V)  divided  by 
the  branch.  If  the  relation  between 
the  resistance  is  the  same  in  each 


Fig.  2 


the 

the 


impedance    of 
reactance    and 


branch,  the  current  in  the  various  branches  will  be  dis- 
placed in  phase  from  the  pressure  indicated  by  the  volt- 
meter (V),  the  same  amount,  or  the  several  branch  currents 
(Ir),  (Ii),  and  (Ic)  will  be  in  phase.  The  current  (I)  indi- 
cated on  the  ammeter  (A)  connected  in  the  main  line  is  the 
numerical  sum  of  the  branch  currents,  when  they  are  all  in 


THE  ALTERNATING-CURRENT  CIRCUIT 


353 


phase,  and  the  vector  sum  when  the  branch  currents  are  not 
in  phase. 

392.  Instantaneous  Power  in  an  Alternating-Current  Circuit. 
— The  instantaneous  power  in  a  circuit  at  any  time  is  equal  to 
the  product  of  the  current 
and  the  e.m.f.  at  that  par- 
ticular instant.  The  two 
curves  (I)  and  (E),  Fig. 
290,  represent  the  current 
in  a  circuit  and  the  e.m.f. 
acting  on  the  circuit.  These 
two  curves  are  in  phase 
and  the  power  in  the  cir- 
cuit is  represented  by  the 
curve  (P),  its  ordinates 
being  proportional  to  the 
product  of  the  ordinate  of 


180         i70 
Fig.  290 


360 


the  other  two  curves.  This 
product  is  positive  in  sign 
at  all  times  since  the 

sign  of  both  the  current  and  the  e.m.f.  changes  at  the  same 
time,  and  both  loops  of  the  curva  (P)  are  drawn  above  the 
horizontal  line.  If  the  current  and  the  e.m.f.  be  displaced  in 

phase,  as  shown  in  Fig.  291, 
the  product  of  their  in- 
stantaneous values  is  not 
positive  throughout  the 
cycle,  but  it  is  negative  in 
sign  fcr  a  portion  of  the 
time  and,  as  a  result,  part 
of  the  curve  (P)  is  below 
the  horizontal  line.  The 
loops  of  the  curve  (P)  above 
the  horizontal  line  represent 
an  output  from  the  source 
of  energy  and  the  loops  be- 
low the  horizontal  line  rep- 
resent an  input  into  the 

source  of  energy.  The  actual  output  then  is  proportional  to 
the  difference  in  area  of  an  equal  number  of  upper  and  lower 
loops.  When  the  current  and  the  e.m.f.  are  in  phase,  there 


354  PRACTICAL  APPLIED  ELECTRICITY 

are  no  lower  loops,  and  the  power  in  the  circuit  might  be 
thought  of  as  all  being  positive.  If  the  current  and  the  e.m.f. 
be  displaced  in  phase  by  90  degrees,  the  upper  and  lower 
loops  are  equal  in  area  and  the  resultant  power  is  zero. 

The  current  in  any  case  may  be  divided  into  two  parts,  one 
part  in  phase  with  the  e.m.f.  and  the  other  part  making  an 
angle  of  90  degrees  with  the  e.m.f.,  or  at  right  angles  to  it. 
The  power  output  due  to  the  part  of  the  total  current  at  right 
angles  to  the  e.m.f.  is  zero,  because  the  area  of  the  upper  and 
the  lower  power  loops  are  equal.  The  part  of  the  total  cur- 
rent in  phase  with  the  e.m.f.  is  all  effective  as  far  as  power 
output  is  concerned,  because  the  power  loops  will  all  be  above 
the  horizontal  line. 

When  the  current  and  the  e.m.f.  are  in  phase,  the  power  is 
equal  to  the  product  of  the  effective  e.m.f.  and  the  current. 
If  the  current  and  the  e.m.f.  are  displaced  in  phase,  the  power 
is  not  equal  to  the  product  of  the  effective  e.m.f:  and  the 
current,  but  the  current  must  be  resolved  into  two  parts,  one 
part  in  phase  with  the  e.m.f.  and  the  other  at  right  angles  to 
the  e.m.f.  The  part  of  the  current  or  component  in  phase 
with  the  e.m.f.  is  equal  to  (I)  times  the  cosine  of  the  angle 
(9)  between  the  current  and  the  e.m.f.  This  component  of 
the  current  times  the  e.m.f.  gives  the  true  power  in  the  cir- 
cuit, or 

Power  in  watts  =  E  I  cos  9  (149) 

in  which  (9)  is  the  angle  between  the  current  and  the  e.m.f. 
and  cos  9  is  called  the  power  factor. 

393.  Determining  the  Value  of  the  Power  Factor. — Since 
the  cosine  of  an  angle  such  as  (9).,  Fig.  128,  is  equal  to  the 
ratio  of  the  line  (c)  to  (b)  or  it  is  equal  to  (c-=-b),  the  power 
factor  of  a  circuit  can  be  easily  determined  when  the  con- 
stants of  the  circuit  are  known.  The  e.m.f.  (E)  and  the  cur- 
rent (I),  Fig.  285,  are  displaced  in  phase  by  the  angle  (9). 
The  line  (RI)  divided  by  the  line  (E)  gives  the  cosine  of  (9), 
or  the  power  factor.  Since  (E)  is  equal  to  (ZI),  and  Z  = 
V  R2  4-  X^  the  value  of  the  cosine  of  (9)  may  assume  a 
Dumber  of  different  forms. 

RI          RI          R             R 
Power   factor  = = =  —  = (150) 


E  ZI          Z        V  R2  4-  X2 


THE  ALTERNATING-CURRENT  CIRCUIT  355 

394.  A  Wattmeter  Indicates  the  True  Power  in  an  Alter- 
nating-Current Circuit. — The  indication  of  a  wattmeter  is  pro- 
portional to  the  strength  of  two  magnetic  fields,  one  of  which 
is  produced  by  the  load  current  and  the  other  by  the  impressed 
pressure.  The  direction  of  these  two  fields  must  bear  a  dif- 
ferent relation  to  each  other  in  order  that  the  deflection  of 
the  moving  system  of  the  wattmeter  be  in  the  proper  direc- 
tion. If  one  field  reverses  due  to  a  reversal  of  the  e.m.f.  or 
current,  the  moving  system  of  the  wattmeter  will  tend  to  move 
over  the  scale  in  the  opposite  direction  to  what  it  did  before 
the  one  field  reversed  in  direction.  If  both  fields  reverse  at 
the  same  time,  the  force  tending  to  deflect  the  moving  system 
does  not  change  in  direction.  A  wattmeter  would  indicate 
zero  power  if  the  force  acting  on  the  moving  system  acted  for 
the  same  time  in  opposite  directions.  This  would  be  the  case 
when  the  e.m.f.  and  the  current  are  displaced  in  phase  by  90 
degrees,  the  upper  and  the  lower  power  loops  being  equal  in 
area.  When  the  current  and  the  e.m.f.  are  in  or  out  of  phase, 
the  indication  of  the  wattmeter  is  proportional  to  the  average 
of  all  the  values  of  the  instantaneous  power  for  a  complete 
cycle,  or  the  instrument  measures  the  true  power.  When  the 
e.m.f.  and  current  are  displaced  in  phase  less  than  90  degrees, 
the  upper  and  the  lower  loops  of  the  power  curve  are  not 
equal.  The  force  acting  on  the  moving  system  corresponding 
to  the  lower  loop  is  opposite  to  the  force  corresponding  to  the 
upper  loop,  and  the  resultant  force  is  thus  proportional  to  the 
difference  in  these  two  forces,  which  causes  an  indication 
corresponding  to  the  true  power. 

The  product  of  the  voltmeter  and  the  ammeter  reading, 
(E)  and  (I),  does  not  give  the  true  power  in  an  alternating- 
current  circuit  unless  the  current  and  the  e.m.f.  are  in  phase. 
The  product  (E  X  I)  is  called  the  apparent  power.  In  general, 
the  wattmeter  reading  (P),  or  true  power,  equals  (E  X  I),  or 
apparent  power  multiplied  by  the  power  factor. 

P  =  E  X  I  X  power  factor  (151) 

Power  factor  =  P  -f-  (E  X  I)  (152) 


356  PRACTICAL  APPLIED  ELECTRICITY 

PROBLEMS    ON    THE    ALTERNATING-CURRENT    CIRCUIT 

1.  A  condenser  of  132-microfarads  capacity  and  an  induct- 
ance of  .061  henry  are   connected  in   series  and   a   60-cycle 
e.m.f.  of  100  volts  is  impressed  upon  the  circuit.     Calculate 
the  inductance  and  the  capacity  reactances,  respectively. 

Ans.     Inductance  reactance    (Xi)  =  23.0   ohms. 
Capacity  reactance        (X,-)  =  20.0   ohms. 

2.  If  a  resistance  of  4  ohms  be  connected  in  series  with 
the  circuit  given  in  problem  1,  what  will  be  the  total  impe- 
dance of  the  circuit?    What  current  will  be  produced  by  the 
impressed  pressure  of  100  volts? 

Ans.     Impedance  of  entire  circuit  (Z)  =    5  ohms. 

Current  (I)  =  20  amperes. 

3.  Two  impedances  are  connected  in  series  and  they  each 
are  composed  of  resistances  of  10  and   12  ohms,  and  react- 
ances of  ' — 50  and  70  ohms.     Calculate  the  total  impedance  of 
the  circuit. 

Ans.     29.7  ohms. 

4.  Calculate  the  admittance  of  a  circuit  having  a  suscept- 
ance  and  conductance  of  3  and  5  mhos,  respectively.    What  is 
the  impedance  of  the  circuit? 

Ans.    Admittance  (Y)  =  5.83  mhos. 
Impedance     (Z)  =  .171  ohm. 

5.  The  indication  of  a  wattmeter  connected  to  a  certain 
load  is  10  000  watts.    An  ammeter  connected  in  the  line  indi- 
cates 125  amperes  and  a  voltmeter  connected  across  the  load 
indicates  100  volts.    What  is  the  impedance  of  the  circuit  and 
the  power  factor? 

Ans.     Impedance          (Z)  =  .8  ohm. 
Power  factor  (PF)  =  .8 

6.  The  effective  value  of  a  sine  alternating  current  is  10 
amperes,  what  are  the  average  and  maximum  values? 

AnSo    Average  current      =    9.00  amperes. 
Maximum  current  =  14.14  amperes. 

7.  A  circuit  having  a  resistance  of  3  ohms  and  a  resultant 
reactance  of  4  ohms  is  connected  to  a  100-volt  line.    Determine, 


THE  ALTERNATING-CURRENT  CIRCUIT  357 

(a)  the  impedance  of  the  circuit,  (b)  power  factor,  (c)  cur- 
rent, (d)  apparent  power,  (e)  true  power. 

(a)  Impedance  (Z)    =  5  ohms 

(b)  Power  factor       =  .6 

Ans.     (c)  Current  =  20  amperes 

(d)  Apparent  power  =  2000  watts 

(e)  True  power         =1200  watts 


CHAPTER  XVIII 

ALTERNATING-CURRENT    MACHINERY 

395.  Alternators. — An  alternator  is  a  machine  for  convert- 
ing mechanical  energy  into  electrical  energy,  which  is  delivered 
as  an  alternating  current  to  a  circuit  connected  to  the  ter- 
minals of  the  machine.    The  fundamental  electrical  principle 
upon  which  the  alternator  operates  is  the  same  as  that  of  the 
direct-current  generator,   namely,   electromagnetic   induction. 
Alternators,  like  direct-current  machines,  consist  of  two  prin- 
cipal parts,  a  magnetic  field  and  an  armature.     The  commu- 
tator of  the  direct-current  machine  is  replaced  in  alternators 
by   slip-rings   which  are  connected  to   the   terminals   of  the 
armature  winding,  and  with  which  brushes  make  continuous 
contact   and   thus   conduct  the   electricity   to   and   from   the 
armature  winding. 

396.  Types   of   Alternators. — Alternators   may   be    divided 
into  three  types,  depending  upon  the  mechanical  arrangement 
of  the  magnetic  field  and  armature,  viz, 

(A)  Alternators  with  stationary  fields  and  revolving  arma- 
tures. 

(B)  Alternators  with  stationary  armatures  and  revolving 
fields. 

(C)  Alternators  with   both   armature  and  field   stationary 
and  using  a  rotating  part  called  the  inductor.     Such  alterna- 
tors are  called  inductor  alternators. 

Small  machines  are  usually  of  the  revolving  armature  type, 
as  the  e.m.f.  generated  is  usually  comparatively  low  and  the 
current  the  brushes  must  carry  is  small  and  no  difficulty  is 
experienced  in  properly  collecting  such  a  current.  A  direct- 
current  generator  can  be  converted  into  a  revolving-armature 
alternator  by  placing  two  collector  rings  on  one  end  of  the 
armature  and  connecting  these  two  rings  to  points  in  the 
armature  winding  that  are  180  electrical  degrees  apart.  Such 

358 


ALTEENATING-CUKEENT  MACHINERY 


359 


a  connection  for  a  two-pole,  ring-wound  armature  is  shown  in 
Fig.  292.     The  commutator  is  not  shown  in  this  figure. 

The  necessity  of  collecting  the 
armature  current  is  overcome  by  mak- 
ing the  armature  the  stationary  part 
and  revolving  the  field  poles,  the  cir- 
cuit of  the  field  winding  being  con- 
nected to  the  source  of  excitation  by 
means  of  collector  rings  and  brushes. 
In  such  machines  the  armature  wind- 
ing is  placed  in  a  laminated  frame 

that  surrounds  the  revolving  field.    A  revolving-field  alterna- 
tor is  shown  in  Fig.  293. 

The  construction  of  the  inductor  alternator  is  such  that 
both  the  armature  and  the  field  are  stationary.  The  reluctance 
of  the  magnetic  circuit  in  this  type  of  machine  is  changed  in 


Fig.  292 


Fig.  293 

value  by  means  of  projecting  arms,  on  a  revolving  mass  of 
iron  called  the  inductor.  The  path  of  the  magnetic  circuit  is 
through  the  armature  coils  and  as  a  result  of  the  reluctance 


360 


PRACTICAL  APPLIED  ELECTRICITY 


of  this  path  changing,  due  to  the  rotation  of  the  inductor, 
there  will  be  a  varying  magnetic  flux  through  the  armature 
winding,  which  will  result  in  an  induced  electromotive  force 
in  the  winding.  This  induced  e.m.f.  will  be  in  one  direction 
for  an  increasing  flux  through  the  armature  coils,  and  in  the 
opposite  direction  for  a  decreasing  flux,  resulting  in  an  alter- 
nating e.m.f. 

Alternators  may  also  be  classified  into  the  following  groups: 

(A)  Single-phase  Alternators. 

(B)  Polyphase  Alternators. 

397.  Single-phase  and  Two-phase  Alternators. — A  single- 
phase  alternator  is  one  that  produces  a  single  electromotive 
force,  and  a  polyphase  alternator  is  one  that  produces  two  or 
more  electromotive  forces,  which  may  or  may  not  produce 
currents  in  circuits  that  are  electrically  independent.  The 
electromotive  forces  in  a  polyphase  alternator  are  related  to 
each  other  only  by  the  element  of  time,  or  they  are  said  to 


90"         180* 

Fig.  294 


\ 


Eb 

Fig.  295 


differ  in  phase.  Thus  in  a  two-phase  alternator,  there  are  two 
electromotive  forces  which  are  displaced  in  phase  by  90  de- 
grees, or  they  are  said  to  be  in  quadrature.  The  armature 
inductors  in  which  these  electromotive  forces  are  induced 
may  or  may  not  form  independent  windings  on  the  armature. 
When  these  windings  are  not  independent,  they  must  each  be 
connected  to  two  independent  collector  rings.  The  e.m.f.'s 
between  these  two  sets  of  rings  can  be  represented  by  two 
curves  (Ea)  and  (Eb),  Fig.  294,  which  are  displaced  in 
phase  by  90  degrees,  or  they  may  be  represented  by  the  two 


ALTEENATING-CUEKENT  MACHINEEY 


361 


vectors  (Ea)  and  (Eb),  Fig.  295,  that  are  at  right  angles 
to  each  other.  The  arrow  (R)  in  Fig.  295  represents  the 
direction  of  rotation.  The  number  of  collector  rings  on 
such  a  machine  can,  however,  be  reduced  to  three,  when 
they  are  independent  windings  on  the  armature,  by  using  one 
ring  as  a  common  connection  for  both  armature  windings. 
Such  an  arrangement  would  constitute  a  two-phase  three-wire 
system  and  the  one  in  the  previous  case  would  be  a  two-phase 
four-wire  system.  In  the  two-phase  three-wire  system,  the 
current  in  the  common  lead  is  equal  to  the  vector  sum 
of  the  currents  in  the  two  outside  leads,  Fig.  296.  When 
there  is  the  same  current  in  each  outside  lead  and  the  same 
phase  relation  exists  between  the  currents  and  their  e.m.f.'s, 
the  system  is  said  to  be  balanced.  The  current  in  the  common 
lead  is  not  zero  for  a  balanced  load,  however,  as  shown  in  Fig. 
296,  it  being  the  vector  sum  of  (Ia)  and  (Ib),  or  it  is  equal 
to  (!„). 

398.  Three-Phase  Alternators. — 
If  three  single-phase  windings  be 
placed  upon  an  armature  core  and 
displaced  120  electrical  degrees 
from  each  other,  the  electromotive 
forces  induced  in  these  three  wind- 
ings will  be  displaced  in  phase  120 
degrees,  as  shown  by  the  curves 
(Ea),  (Ei,),  and  (Ec),  in  Fig.  297, 
and  by  the  vectors  (A),  (B)  and 
(C)  in  Fig.  298.  Each  of  these 
windings  may  be  provided  with  two 
slip-rings,  there  being  six  in  all, 
and  connected  to  electrically  inde- 
pendent circuits.  Such  a  system 
would  constitute  a  three-phase  six- 
wire  system.  The  three  circuits  connected  to  the  differ- 
ent phases  may  be  kept  practically  independent  of  each 
other  by  using  four  leads  and  connecting  three  of  the  col- 
lector rings  together,  as  shown  in  Fig.  299.  The  lead  (4) 
serves  as  a  common  return  to  the  other  three.  When  the 
three  receiving  circuits  connected  between  the  mains  (1),  (2), 
(3),  and  (4)  have  the  same  resistance  and  reactance,  the 
system  is  said  to  be  balanced  and  the  current  in  the  three 


Fig.  296 


362 


PRACTICAL  APPLIED  ELECTRICITY 


circuits  are  equal  and  displaced  in  phase  from  their  electro- 
motive forces  by  the  same  angle,  the  three  currents  are  then 
120  degrees  apart  and  their  vector  sum,  which  is  the  current 
in  main  (4),  is  zero.  Hence,  for  a  balance  load,  main  (4) 
carries  no  current,  and  this  lead  can  be  dispensed  with  and 
only  three  collector  rings  need  be  used,  the  other  three  being 
connected  together,  forming  what  is  called  the  neutral  point. 


o*'    360° 


Fig.  297 


This  arrangement  of  connections  is  called  the  "Y"  or  "star" 
scheme  of  connecting  the  three  windings.  Three  of  the  six 
rings  can  be  dispensed  with  entirely,  one  terminal  of  each  of 
the  windings  being  connected  to  the  neutral  point  inside  the 

armature,  as  shown  in  the 
symmetrical  diagram  in 
Fig.  300. 

Another  method  of  con- 
necting the  three  wind- 
ings of  a  three-phase  ma- 
chine is  shown  in  Fig.  301, 
which  js  called  the  "A" 
(delta)  or  "mesh"  scheme. 
399.  Relation  of  E.M.F. 


Fig.  299 


and    Current    in    "Y"    and 


"A"  Connected  Armatures. — The  currents  in  the  mains  (1), 
(2),  and  (3),  Fig.  300,  are  the  same  as  the  currents  in  the 
three  windings  (A),  (B),  and  (C). 

If  the  positive  direction  of  the  electromotive  forces  and  cur- 
rents in  the  windings  (A),  (B),  and  (C)  be  taken  in  the  direc- 
tion indicated  by  the  arrows  in  Figs.  300  and  301,  then  the 


ALTERNATING-CURRENT  MACHINERY 


363 


e.m.f.  between  the  mains  (1)  and  (2)  in  Fig.  300  will  be  equal 
to  the  vector  difference  between  the  e.m.f.'s  in  windings  (A) 
and  (B).  (It  must  be  remembered  that  the  direction  of  the 
arrows  does  not  represent  the  actual  direction  of  the  e.m.f.'s 
and  currents,  but  only  the  assumed  positive  direction.)  The 
vector  difference  between  the  two  e.m.f.'s  in  the  windings  (A) 
and  (B),  which  are  displaced  in  phase  by  120  degrees,  is  ob- 


Fig.  300 


Fig.  301 


tained  by  reversing  the  direction  of  the  vector  (B)  and  adding 
it  to  the  vector  (A),  giving  the  result  (A  —  B),  Fig.  302.  The 
e.m.f.'s  between  leads  (2)  and  (3),  and  (3)  and  (1)  are  ob- 
tained in  a  similar  manner.  These  resultant  e.m.f.'s  will  be 
equal  to  V~3~times  the  e.m.f.  in  any  one  of  the  windings,  which 
can  be  shown  by  reference  to  Fig.  303.  (Ei)  represents  the 
e.m.f.  in  winding  (A)  and  ( — Ei.)  represents  the  e.m.f.  in  wind- 
ing (B).  Assuming  (Ea)  and  (Eb)  are  each  equal  to  2  units 
of  e.m.f.,  then  (a)  will  represent  1  unit  and  (d)  will  represent 
VlTunits  of  e.m.f.  Two  (d),  which  is  equal  to  (A  — B),  will 
be  equal  to  (2  V  3)  units  of  e.m.f.  when  (Ea)  and  (Eh)  are 
equal  to  2  units  of  e.m.f.  Hence  (A  —  B)  is  equal  to  the  V~3 
times  the  e.m.f.  per  winding. 

The  e.m.f.  between  leads  (1)  and  (3),  Fig.  301,  is  the  same 
as  the  e.m.f.  in  the  winding  (A),  or  the  e.m.f.  between  leads 
for  the  "A"  connection  is  equal  to  the  e.m.f.  in  the  winding 
connected  to  the  two  leads.  The  current  in  lead  (1)  is  equal 
to  the  vector  difference  between  the  currents  in  windings  (A) 
and  (B).  These  two  currents  are  displaced  in  phase  120 
degrees  and  their  difference  is  obtained  by  reversing  (B)  and 
adding  it  to  (A).  The  current  in  the  other  leads  are  obtained 


364 


PRACTICAL  APPLIED  ELECTRICITY 


in  a  similar  manner  and  for  a  balance  load  the  current  in  any 
lead  will  be  equal  to  V~3~times  the  current  in  any  winding. 

400.  Connecting  Receiving  Circuits  to  a  Three-Phase  System. 
— When  the  receiving  circuits  connected  to  the  various  phases 
of  a  three-phase  system  are  dissimilar  or  take  unequal  current, 
resulting  in  an  unbalanced  load,  four  mains  should  be  used, 


Fig.  302 


Fig,  303 


as  indicated  in  Fig.  299,  each  receiving  circuit  then  takes  cur- 
rent from  one  of  the  windings  (A),  (B),  or  (C)  over  the  main 
(4)  and  one  of  the  outside  mains.  It  is  always  desirable, 
however,  in  the  operation  of  alternators  to  keep  the  loads  on 
the  various  phases  as  near  equal  as  possible  and  in  practice 
the  different  receiving  circuits  are  so  distributed  between  the 
three  phases  as  to  satisfy  this  condition  as  nearly  as  possible. 
If  three  single-phase  motors,  all  of  the  same  capacity  and 
carrying  the  same  load,  be  operated  from  the  three  phases  of 
a  three-phase  system,  the  system  will  be  balanced  and  no  cur- 
rent will  exist  in  the  lead  (4)  when  the  connections  are  made 
as  shown  in  Fig.  299.  Three  lighting  circuits  taking  equal 
currents  will  result  in  the  same  condition.  If,  however,  one 
of  the  motors  or  one  of  the  lighting  circuits  be  disconnected, 
there  will  then  be  a  current  in  lead  (4). 

When  the  output  of  the  three-phase  alternator  is  used  to 
drive  three-phase  induction  motors,  synchronous  motors,  and 
synchronous  converters,  the  currents  in  each  of  the  three 
windings  will  be  equal  and  will  be  displaced  in  phase  from 
their  respective  e.m.f.'s  by  the  same  angle,  or  the  system  is 
balanced.  For  balanced  load  only  three  leads  are  required  and 


ALTERNATING-CURRENT  MACHINERY 


365 


either  the  "Y"  connection  without  the  neutral,  as  shown  in 
Fig.  300,  or  the  "A"'  connection,  as  shown  in  Fig.  301,  may 
be  employed. 

The  current  in  each  receiving  circuit  in  Fig.  304  is  equal  to 
the  current  in  the  lead  connected  to  it,  and  the  e.m.f.  over  any 
one  of  the  receiving  circuits  in  Fig.  305  is  equal  to  the  e.m.f. 
between  the  leads  connected  to  that  particular  receiving  cir- 
cuit. The  current  in  each  receiving  circuit  in  Fig.  305  is 
equal  to  the  current  in  each  lead  divided  by  the  V"sTand  the 
e.m.f.  over  each  receiving  circuit  in  Fig.  304  is  equal  to  the 
e.m.f.  between  leads  divided  by  the  V  3. 

401.  Measurement  of  Power  in  Single-Phase  System. — The 
connections  for  the  measurement  of  power  in  a  single-phase 


Neutral 


Fig.  304 


Fig.  305 


system  are  identical  to  those  for  the  measurement  of  power 
in  a  direct-current  circuit.  The  connections  of  a  Weston  indi- 
cating wattmeter  are  given  in  Fig.  306.  The  alternator  (A) 
is  supplying  energy  to  the  lamps  (L)  as  a  load. 

402.  Measurement  of  Power  in  a  Two-Phase  System. — In  a 
two-phase  four-wire  system,  the  power  is  measured  in  each  of 
the  two  phases  by  separate  wattmeters  as  though  they  were 
single-phase  circuits  and  the  total  power  is  obtained  by  adding 
the  two  wattmeter  readings. 

In  a  two-phase  three-wire  system,  the  power  may  be  meas- 
ured by  two  wattmeters,  they  being  connected  as  shown  in  Fig. 
307.  When  the  connections  are  thus  made,  the  upper  watt- 
meter indicates  the  power  in  phase  (A)  and  the  lower  watt- 
meter indicates  the  power  in  phase  (B).  The  total  power 


366 


PRACTICAL  APPLIED  ELECTRICITY 


at  any  instant  is  equal  to  the  sum  of  the  indications  on  the 
two  wattmeters. 

A  single  wattmeter  may  be  used  to  measure  the  power  in  a 
two-phase  circuit  by  connecting  its  current  coil  in  the  common 
lead,  as  shown  in  Fig.  308,  and  then  noting  its  indication  first, 
when  the  pressure  circuit  is  connected  to  one  outside  lead, 

Current  Coil 


*/5®®P] l       . 

r^sinnmr  6666 

DT-^CO..^^  r~;\ 


Pressure  Coil 


Load 


Fig.  306 


Current  Coil 
Fig.  307 


as  shown  by  the  full  line  in  the  figure,  and  second,  when  the 
pressure  circuit  is  connected  to  the  other  outside  lead,  as 
shown  by  the  dotted  line  in  the  figure.  If  the  load  on  the  two 
phases  remain  constant  while  these  two  readings  are  being 
taken,  the  total  power  output  of  the  two-phase  machine  will 
be  equal  to  the  sum  of  the  two  wattmeter  indications. 

When  the  pressure  circuit 

_  _  is    corrected    as    shown    by 

the  dotted  line,  the  watt- 
meter will  not  indicate  the 
power  delivered  by  phase 
(A),  nor  will  it  indicate  the 


Common 


Current  Coil 


555 


power    delivered    by    phase 
(B)  when  the  pressure  con- 
Fig.  308  nection   is   made   as    shown 
by  the  full  line,  unless  the 

current  in  each  phase  is  in  phase  with  its  e.m.f.  The  rea- 
son for  this  can  be  shown  by  referring  to  Fig.  296, 
in  which  (Ba)  and  (Eb)  represent  the  e.m.f.'s  of  phases 
(A)  and  (B),  (Ia)  and  (Ib)  represent  the  currents  in 
the  two  phases,  and  these  currents  are  shown  displaced 
in  phase  from  their  e.m.f.'s  by  the  angles  (6^  and  (92). 
The  current  in  the  common  lead,  or  in  the  current  coil  of  the 
wattmeter,  is  represented  by  the  vector  (In),  which  is  the 


THE  ALTEKNATING-CUEKENT  CIKCUIT  367 

resultant  of  (Ia)  and  (Ib).  When  the  pressure  coil  is  con- 
nected across  phase  (A),  the  wattmeter  indication  is  equal  to 
(Ea  X  !„  X  sin  93).  The  product  of  (In)  and  (sin  O3)  is  equal 
to  the  component  of  (In)  that  is  in  phase  with  (Ea).  The 
indication  of  the  wattmeter  when  the  pressure  connection  is 
across  phase  (B)  is  equal  to  (Ei,  X  In  X  cosB3).  The  product 
of  (In)  and  (cos  0,)  is  equal  to  the  component  of  (In)  that 
is  in  phase  with  (Eb).  If  the  component  of  (In)  in  phase 
with  one  of  the  e.m.f.'s,  say  (Ea),  is  equal  to  the  current  in 
phase  (A),  then  the  wattmeter  will  indicate  the  power  in 
phase  (A)  when  the  pressure  connection  is  made  as  shown  by 
the  dotted  line.  The  component  of  (In)  in  phase  with  (Ea) 
will  be  equal  to  (L)  only  when  the  currents  in  the  two 
phases  are  in  phase  with  their  e.m.f.'s. 

403.  Measurement  of  Power  in  a  Three-Phase  System. — The 
power  in  a  three-phase  six-wire  system  can  be  measured  as 
though  it  were  three  single-phase  circuits,  which  in  reality 

it  is.     The  total  power  out- 

I       ./ooonoorv^ put   of    a    macnine    then    is 

~~^?  equal  to  the  sum  of  the 
wattmeter  indications  in  the 
three  phases.  In  a  three- 
phase  four-wire  system  the 

power  per  Phase  can  be  de' 
termined    by    connecting    a 
wattmeter    in    each    of    the 
Fig.  309  leads  (1),  (2),  and  (3),  and 

connecting  their  pressure 

circuits  between  these  leads  and  the  neutral  lead  (4),  Fig.  299. 
The  total  power  output  is  equal  to  the  sum  of  the  three  watt- 
meter indications.  In  a  three-phase  three-wire  system,  the 
power  per  phase  can  be  determined  by  connecting  three  watt- 
meters as  shown  in  Fig.  309.  The  total  power  output  of  the 
three  phases  is  equal  to  the  sum  of  the  three  wattmeter  indi- 
cations. The  above  connection  will  apply  equally  well  when 
the  receiving  circuit  is  connected  "Y"  or  "A»"  provided  the 
series  coils  are  connected  in  series  with  each  load  and  the 
pressure  coils  across  the  loads. 

Two  wattmeters  may  be  used  in  measuring  the  power  in  a 
three-phase  three-wire  system  by  connecting  them  as  shown 
in  Fig.  310. 


368  PRACTICAL  APPLIED  ELECTRICITY 

The  sum  of  the  two  wattmeter  readings  is  the  total  power 
delivered  to  the  three  receiving  circuits.  When  the  power 
factor  is  below  .5,  the  reading  of  one  wattmeter  will  be  nega- 
tive and  the  total  power  is  then  equal  to  the  algebraic  sum  or 
numerical  difference  of  the  two  readings. 

All  of  the  above  connections  apply  to  either  balanced  or 
unbalanced  loads,  making  them  applicable  to  any  practical 
case. 

If  the  system  is  balanced,  only  one  wattmeter  need  be  used 
in  Fig.  309,  and  its  indication  multiplied  by  three  will  give  the 
total  power,  since  on  a  balanced  load  each  of  the  wattmeters 
will  indicate  the  same.  The  power  in  any  balanced  three- 
phase  three-wire  system  is  equal  to  ( V~3~X  E  X  I  X  cos  6), 
(E)  being  the  e.m.f.  between  leads,  (I)  the  current  in  each 
lead,  and  (cos  9)  the  power  factor. 

The  power  factor  of  a  balanced  three-phase  circuit  can  be 
determined  from  the  two  wattmeter  readings,  when  they  are 
connected  as  indicated  in  Fig.  310,  as  follows: 

_Pi-P2 
Tangent  6  =  V  3 (153) 

Pi  +  P2 

Substituting  the  values  of  (Pj),  which  is  the  larger  reading 
and  will  always  be  positive,  and  (P2),  which  is  the  smaller 
reading  and  may  be  positive  or  negative  in  the  above  equation, 

gives  the  value  of  the  tan- 
Current  Coil  sent   of    (0).      The    angle 

<e>   can  tnen  be  deter- 

mined  from  the  table  of 
trigonometric  functions, 
Chapter  20,  and  the  cosine 
of  this  angle  is  the  power 
factor. 

Current  Coil  404.     The     Synchronous 

Fig.  310  Motor. — In  the  operation  of 

an  alternating-current  gen- 
erator, a  mechanical  force  must  be  applied  to  rotate  the 
moving  part  of  the  machine,  and  when  a  given  conductor 
on  the  armature  is  under  a  north  pole  of  the  field,  the 
current  in  the  conductor  is  in  such  a  direction  that  the  mag- 
netic field  exerts  a  force  on  it  which  opposes  the  movement  of 
the  conductor  or  the  rotation  of  the  armature.  If  the  conductor 


ALTERNATING-CURRENT  MACHINERY 

moves  out  of  the  field  of  a  north  pole  and  into  the  field 
of  a  south  pole,  the  current  will  be  opposite  in  direc- 
tion and,  as  a  result,  there  is  still  a  force  acting  on  the  con- 
ductor which  opposes  the  rotation  of  the  armature.  If  the 
current  output  of  the  generator  increases,  this  opposing  force 
increases  and  more  mechanical  power  must  be  supplied  to 
drive  the  machine. 

If  the  field  of  an  alternator  be  excited  by  a  direct  current, 
and  an  alternating  current  from  some  external  source  be  sent 
through  its  armature,  which  is  revolved  by  an  engine  or  motor 
at  such  a  speed  that  a  given  inductor  in  the  winding  passes 
from  a  certain  position  under  a  north  pole  to  a  corresponding 
position  under  the  next  north  pole  during  the  time  of  one 
cycle,  the  motion  of  the  armature  will  be  aided  by  the  cur- 
rent when  the  direction  of  the  current  is  such  that  the  force 
exerted  by  the  magnetic  field  upon  the  various  conductors  aids 
the  motion.  Since  the  current  reverses  in  direction  when 
the  inductor  passes  from  one  pole  to  the  adjacent  pole,  which 
is  of  opposite  polarity,  the  force  exerted  by  the  magnetic  field 
upon  the  conductor  remains  constant  in  direction.  If  the 
speed  of  the  alternator  has  been  adjusted  so  that  the  above 
conditions  are  fulfilled,  the  engine  or  motor  may  be  discon- 
nected and  the  alternator  will  continue  to  revolve  at  a  con- 
stant speed,  which  is  determined  by  the  frequency  of  the 
supplied  current  and  the  number  of  poles  comprising  the  mag- 
netic field  of  the  motor.  When  an  alternator  is  operated  in 
the  above  manner  it  may  deliver  power  to  some  load  by  means 
of  a  belt  or  direct  connection,  and  it  is  called  a  synchronous 
motor. 

Synchronous  motors  are  designed  to  operate  on  single-phase 
or  polyphase  circuits,  their  operation,  however,  is  more  satis- 
factory on  polyphase  circuits.  Motors  of  this  kind  are  called 
synchronous  because  they  run  in  synchronism  with  the  source 
of  supply.  Their  speed  is  not  necessarily  the  same  as  that  of 
the  generator  driving  them,  it  being  the  same  only  when  the 
motor  and  the  generator  have  the  same  number  of  poles.  The 
Speed  of  a  synchronous  motor  can  be  determined  by  the  use 
Of  the  equation 

2  X  f  X  60 
S  = (154) 


370  PRACTICAL  APPLIED  ELECTRICITY 

In  the  above  equation  (f)  is  the  frequency  of  the  impressed 
voltage,  (p)  is  the  number  of  poles  on  the  motor,  and  (S)  is 
the  speed  of  the  motor  in  revolutions  per  minute. 

405.  Operation  of  a  Synchronous  Motor. — The  synchronous 
motor  does  not  behave  in  the  same  way  as  a  direct-current 
motor.     For  example:     If  the  field  of  a  direct-current  motor 
be  weakened,  the  motor  will  speed  up  in  order  that  its  counter- 
electromotive  force  may  reach  the  proper  value.     When  the 
field  of  a  synchronous  motor  is  weakened,  there  is  no  change 
in  its  speed,  since  the  motor  must  run  in  synchronism  with 
the  impressed   e.m.f.       A  change  in  load  on  a   synchronous 
motor  Or  a  change  in  field  strength  will  result  in  a  change  in 
the  phase  displacement  of  the  armature  current  and  the  im- 
pressed voltage      When  the  motor  is  operating  without  load, 
the  field  current  can  be  adjusted  to  such  a  value  that  the  cur- 
rent taken  by  the  motor  is  very  small  and  its  counter  e.m.f. 
is    practically   in   opposition   to   the   impressed    voltage.    An 
increase  in  field  current  will  cause  the  armature  current  to 
lead  the  impressed  voltage,  and  a  decrease  in  field  current  will 
cause  the  armature  current  to  lag  the  impressed  voltage.     If  a 
load  be  placed  on  a  synchronous  motor,  its  armature  will  lag 
a  small  amount  behind  the  alternator  driving  it,  and  this  angle 
will  increase  with  an  increase  in  the  load.     When  the  arma- 
ture of  the  motor  lags,  the  counter-electromotive  force  is  no 
longer  in  opposition  to  the  impressed  e.m.f.  and  a  current  will 
be  produced  which  is  just  sufficient  to  supply  the  required 
torque  to  enable  the  motor  to  carry  its  load.     By  increasing 
the  load,  the  displacement  of  the  armature  will  become  suffi- 
ciently great  to  cause  the  motor  to  be  thrown  out  of  synchron- 
ism, or  it  will  "break  down"  and  stop. 

406.  Starting    Synchronous    Motors. — A    single-phase    syn- 
chronous motor  cannot  be  started  from  rest  by  sending  an 
alternating  current  through  its  armature,  the  field  being  ex- 
cited by  a  direct  current,  because  the  current  in  the  armature 
is  rapidly  reversing  in  direction  and  tends  to  cause  the  arma- 
ture to  rotate  first  in  one  direction  and  then  in  the  other  direc- 
tion.      Single-phase    synchronous    motors    must    always    be 
brought  up  to  full  speed  by  some  outside  source  of  power,  such 
as  another  motor  or  engine,  before  they  can  be  connected  to 
the  source  of  electrical  power. 

The  polyphase  synchronous  motor  may  be  started  by  con- 


THE  ALTERNATING-CURRENT  CIRCUIT  371 

necting  its  armature  directly  to  the  line,  the  field  circuit  of 
the  machine  being  open.  When  the  machine  has  reached 
synchronous  speed,  the  field  circuit  can  be  closed  and  the  load 
gradually  thrown  on.  The  motor  is  usually  connected  to  its 
load  by  means  of  a  friction  clutch.  This  method  of  starting 
synchronous  motors  has  the  great  disadvantage  that  the 
machine  takes  an  exceedingly  large  lagging  current  and  this 
causes  an  excessive  drop  in  the  supply  lead 
and  a  general  disturbance  of  the  distributing 
system.  The  taking  of  a  large  current  from  the 
line  can  be  avoided  by  the  use  of  an  auto-starter  1  L,  I i_t  IL 
or  compensator.  The  operation  of  an  auto- 
starter  is  described  briefly  in  section  (415). 

Very  large  synchronous  motors  are  usually 
started  by  means  of  an  induction  motor  that 
can  be  operated  from  the  same  line  the  syn-c 
chronous  motor  is  operated  from,  or  by  means 
of  a  small  engine  or  direct-current  motor,  on 
account  of  the  very  small  torque  exerted  by  the 
armature  when  it  is  connected  to  the  line. 

407.  Synchronizing. — In  order  that  an  alter-  Fig.  311 
nator  or  a  synchronous  motor  may  be  connected 
to  a  line,  it  must  be  in  synchronism.  Synchronizing  con- 
sists in  adjusting  the  frequency,  the  phase  relation  of  two 
e.m.f.'s  and  their  magnitude  so  that  they  will  coincide  when 
connected  together.  The  general  practice  in  synchronizing  is 
first  to  adjust  the  speed  of  the  incoming  machine  until  the 
frequency  of  its  e.m.f.  corresponds  to  the  frequency  of  the 
line  to  which  it  is  to  be  connected,  then  to  adjust  the  field 
current  until  the  machine  and  the  line  voltage  are  the  same. 
Adjust  the  phase  relation  of  the  incoming  machine  until  it  is 
in  phase  with  the  line,  which  can  be  determined  by  means  of 
lamps,  a  synchronoscope,  or  a  voltmeter,  and  when  they  are 
in  phase,  they  may  be  connected  directly  together. 

When  lamps  are  used  in  synchronizing,  they  should  be  con- 
nected as  shown  in  Fig.  311,  one  in  each  phase.  The  switch 
should  be  so  arranged  that  it  can  be  closed  the  instant  the 
machines  are  in  phase  and  synchronism,  viz,  when  the  lamps 
are  dark.  Two  transformers  may  be  used  with  their  primaries 
connected  across  the  same  leads  but  on  opposite  sides  of  the 
paralleling  switch.  Their  secondaries  may  be  connected  so 


372 


PRACTICAL  APPLIED  ELECTRICITY 


that  their  e.m.f.'s  are  in  series  or  in  opposition  when  the  two 
machines  are  in  phase  and  synchronism.  When  they  are  in 
opposition  and  a  lamp  in  circuit,  the  lamp  will  be  dark  when 
the  machines  are  in  phase  and  synchronism,  and  if  they  are 
connected  in  series  the  lamp  will  be  light. 

The  synch ronoscope  is  an  instrument  that  gives  an  indica- 
tion of  the  phase  relation  of  two  e.m.f.'s,  and  the  one  of 
higher  frequency  can  be  determined  by  noting  the  direction 
in  which  the  pointer  on  the  instrument  rotates. 

In  synchronizing  machines  it  is  always  best  to  close  the 
main  switch  when  the  incoming  machine  is  coming  into 
proper  phase  rather  than  going  out  of  it,  as  the  inertia  of 
the  armature  in  one  case  assists  and  in  the  other  retards 
prompt  synchronizing. 

408.  The  Transformer. — The 
transformer  in  its  simplest  form 
consists  of  two  separate  and  elec- 
trically independent  coils  of  wire 
that  are  wound  upon  a  laminated 
iron  core  that  is  common  to  both 
of  the  windings.  One  of  the 
coils  is  connected  to  some  source 
of  electrical  energy  which  may 
be  high  or  low  voltage,  and  re- 
ceives an  alternating  current  from  it;  and  the  other  coil  is 
connected  to  a  load  to  which  it  delivers  alternating  current  at 
a  low  or  high  voltage.  The  coil  of  the  transformer  that  is 
connected  to  the  source  of  energy  is  called  the  primary  coil, 
and  the  one  that  is  connected  to  the  load  is  called  the  sec- 
ondary coil,  Fig.  312.  When  the  transformer  delivers  energy 
at  a  higher  voltage  than  that  impressed  upon  the  primary 
coil,  it  is  called  a  step-up  transformer;  when  it  delivers  energy 
at  a  lower  voltage  than  that  impressed  upon  the  primary  coil, 
it  is  called  a  step-down  transformer. 

409.  Action  of  the  Transformer  without  Load. — A  trans- 
former is  said  to  be  operating  on  zero  load  when  the  sec- 
ondary circuit  is  open  and  it  is,  of  course,  delivering  no  cur- 
rent. When  there  is  no  current  in  the  secondary  winding, 
there  is  a  very  small  current  in  the  primary  winding  for  the 
following  reason:  The  current  in  the  primary  winding  will 
cause  an  alternating  magnetic  field  to  be  set  up  through 


Primary         Secondary 
Fig.  312 


THE  ALTERNATING-CURRENT  CIRCUIT  373 

both  the  primary  and  the  secondary  windings,  which  induces 
an  electromotive  force  in  both  of  them.  This  induced  e.m.f.  is 
in  the  opposite  direction  to  the  e.m.f.  impressed  upon  the 
primary  winding  and  very  nearly  equal  to  it.  It  is  only  this 
difference  in  e.m.f.  that  is  available  for  producing  a  current 
in  the  primary  winding,  and  since  this  difference  is  small, 
there  will  be  a  small  current  in  the  primary  winding  when 
there  is  no  load  on  the  transformer.  This  current  is  called 
the  no-load  current  of  the  transformer.  The  induced  e.m.f. 
In  the  secondary  coil  is  in  phase  with  the  e.m.f.  induced  in 
the  primary,  and  it  is  in  opposition  to  the  impressed  e.m.f. 
on  the  primary,  or  the  primary  and  the  secondary  e.m.f.'s  are 
displaced  in  phase  by  180°. 

410.  Action    of    the    Transformer    on    Load. — If    the    sec- 
ondary coil  of  a  transformer  be  connected  to  a  receiving  cir- 
cuit and  a  delivering  current,  the  transformer  is  said  to  be 
loaded.     Since   the   e.m.f.   induced  in   the   secondary   coil   is 
180°  from  the  impressed  e.m.f.  on  the  primary  coil,  the  cur- 
rent in  the  secondary  coil  will  produce  a  magnetizing  effect 
which  tends  to  lessen  that  produced  by   the   small  current 
already  in  the  primary  coil  and,  as  a  result,  the  variations  in 
the  magnetic  flux  passing  through  both  of  the  coils   is  de- 
creased, which   results  in  a  decrease  in  the  induced  e.m.f. 
in    the    two    coils.      This    decrease    in    counter   e.m.f.    in   the 
primary  coil  results  in  an  increase  in  the  difference  between 
the  impressed  e.m.f.  and  the  counter  e.m.f.,  which  results  in 
an  increase  of  current  in  the  primary  coil.    If  the  load  on  the 
secondary  coil  be  increased  or  decreased  there  will  be  a  pro- 
portional increase  or  decrease  of  current  in  the  primary  coil. 

411.  Ideal    Electromotive    Force   and   Current    Relations    in 
a  Transformer. — Neglecting  all  losses  in  the  transformer,  the 
following  relations  will  exist  between  the  primary  and  the 
secondary  e.m.f.'s  and  the  primary  and  the  secondary  currents. 
Since   it  is   assumed   that  the   same    magnetic    flux    passes 
through  both  the  coils,  the  ratio  of  the  induced  e.m.f.'s  in  the 
two  coils  must  be  the  same  as  the  ratio  between  the  number 
of   turns   in   the   two    windings.      The   induced   e.m.f.    in   the 
primary  is  equal  to  the  impressed  e.m.f.  when  all  losses  are 
neglected,  and  then 


374  PRACTICAL  APPLIED  ELECTRICITY 

EP       Np 

(155) 
Es       NS 

Since  the  magnetizing  action  of  the  ampere-turns  in  the  two 
coils  are  equal  and  opposite,  neglecting  all  losses,  we  have 

NpIp  =  NsIs  (156) 

or 

IP       Ns 

(157) 

Is  Np 

The  above  equation  states  that  the  primary  and  the  second- 
ary currents  are  to  each  other  inversely  as  the  number  of 
turns  in  the  two  coils. 

412.  Actual  Electromotive  Force  and  Current  Relations  in 
a  Transformer. — In  the  previous  section  the  relation  of  the 
e.m.f.'s  and  the  currents  was  based  upon  the  assumption  that 
there  were  no  losses  in  the  transformer,  which  is  not  the 
case  in  practice.  The  principal  losses  to  consider  in  the 
practice!  operation  of  a  transformer  are: 

(A)  Loss  due  to  no-load  current. 

(B)  The  I2R  loss  in  the  primary  and  the  secondary  coils. 

(C)  Loss  due  to  magnetic  leakage. 

The  part  of  the  no-load  current  in  phase  with  the  impressed 
e.m.f.  on  the  primary  coil  represents  a  loss,  and  it  is  the  no- 
load  current  that  affects  the  ideal  relation  between  the  pri- 
mary and  the  secondary  currents,  as  given  in  equation  (157). 
The  resistance  of  the  primary  and  the  secondary  coils  and 
magnetic  leakage  are,  on  the  other  hand,  the  only  things  that 
affect  to  any  extent  the  ideal  relation  between  the  primary 
and  the  secondary  voltages.  If  all  of  the  magnetic  flux  created 
by  the  current  in  either  the  primary  or  the  secondary  coils 
passed  through  the  other  coil,  there  would  be  no  magnetic 
leakage,  which  would  correspond  to  an  ideal  magnetic  circuit. 
Magnetic  leakage  in  its  effect  is  equivalent  to  an  outside  in- 
ductance that  is  connected  in  series  with  the  coils  of  the 
transformer.  If  this  inductance  be  represented  by  (L),  then 
the  e.m.f.  required  to  overcome  it  when  there  is  a  current  of 
(I)  amperes  in  the  circuit  is  equal  to  (27rfLI).  The  effect  of 
coil  resistance  and  magnetic  leakage  upon  the  ideal  relation 
between  the  primary  and  the  secondary  voltages  is  shown  by 
means  of  a  vector  diagram. 


THE  ALTERNATING-CURRENT  CIRCUIT 


375 


413.  Vector  Diagram  of  a  Transformer. — The  magnetic 
flux  that  passes  through  both  the  primary  and  the  secondary 
coils  is  represented  by  the  vector  (<f>),  as  shown  in  Fig.  313, 
and  the  no-load  current  by  the  vector  (I0).  The  e.m.f.  induced 
in  the  primary  and  the  secondary  coils  will  lag  the  magnetic 
flux  (*)  90°. 

The  e.m.f.  impressed  upon  the 
primary  coil  is  used  in  overcom- 
ing the  resistance  of  the  coil,  the 
counter  e.m.f.  induced  in  the  coil 
by  the  flux  ($),  which  passes 
through  both  coils,  and  the  effect 
of  magnetic  leakage.  The  e.m.f. 
to  overcome  the  resistance  is  in 
phase  with  the  primary  current 
(IP),  as  shown  in  the  figure,  the 
vector  (EP)  represents  the  e.m.f. 
required  to  overcome  the  e.m.f. 
induced  in  the  primary  coil  by 
the  flux  ($),  and  the  vector 
(2irfLPIp)  represents  the  e.mf. 
required  to  overcome  the  effect 
of  magnetic  leakage  in  the  pri- 
mary, which  is  90  degrees  in 
advance  of  the  primary  current. 
The  vector  (Ep)  represents  the 

voltage  impressed  upon  the  primary  coil.  The  voltage  induced  in 
the  secondary  winding  is  represented  by  the  vector  (Es),  which 
bears  the  same  relation  to  the  e.m.f.  induced  in  the  primary 
coil  as  exists  between  the  primary  and  the  secondary  turns, 
which  has  been  assumed  unity  in  this  case.  This  vector  will 
represent  the  voltage  at  the  terminals  of  the  secondary  coil 
when  there  is  no  load  on  the  transformer.  When  the  sec- 
ondary coil  is  supplying  a  current,  the  terminal  voltage  drops 
on  account  of  the  (LRs)  drop  and  magnetic  leakage.  These 
drops  must  be  subtracted  from  the  total  e.m.f.  induced  in 
the  secondary  coil,  which  gives  the  terminal  voltage  equal  to 
(Es).  The  drop  (RSIS)  is  parallel  to  (Is),  and  the  drop 
(27rfLsIs)  is  perpendicular  to  (Is).  If  the  secondary  coil  is 
supplying  a  current  (Is)  there  will  be  a  current  in  the  primary 


376 


PRACTICAL  APPLIED  ELECTRICITY 


coil,  which  combines  with  the  no-load  current  (I0),  giving  the 
true  primary  current  (I). 

414.  Types  of  Transformers. — Transformers  may  be 
divided  into  two  types,  depending  upon  the  arrangement  of 
the  coils  and  magnetic  circuit,  viz, 

(A)  Core-type  transformers. 

(B)  Shell-type  transformers. 

In  the  core-type  transformer  the  coils  are  placed  outside  of 
the  magnetic  circuit,  as  shown  in  Fig.  314.  In  the  shell-type 
transformer  the  magnetic  circuit  surrounds  the  coils,  as 
shown  in  Fig.  315. 

Transformers  may  be  divided  into  two  types,  depending 
upon  the  kind  of  circuit  they  are  to  be  used  on,  viz, 

(A)  Single-phase  transformers. 

(B)  Polyphase  transformers. 


Fig.  314 


Fig.  315 


In  a  single-phase  transformer  there  is  only  one  set  of  pri- 
mary and  secondary  terminals,  and  the  fluxes  in  the  one  or 
more  magnetic  circuits  are  all  in  phase.  In  the  polyphase 
transformer  there  are  a  number  of  different  sets  of  primary 
and  secondary  connections.  These  various  sets  can  be  used  in 
the  different  phases  of  a  polyphase  system.  In  such  a  trans- 
former there  are  two  or  more  magnetic  circuits  through  the 
core,  and  the  fluxes  in  the  various  circuits  are  displaced  in 
phase.  It  is  not  necessary  to  always  use  polyphase  trans- 
formers in  polyphase  circuits,  as  a  number  of  single-phase 
transformers  may  be  used,  one  in  each  phase. 

Transformers  may  be  divided  into  three  types,  depending 
upon  the  nature  of  their  output,  viz, 


THE  ALTERNATING-CURRENT  CIRCUIT  377 

(A)  Constant-potential  transformers. 

(B)  Constant-current  transformers. 

(C)  Current  transformers. 

The  constant-potential  transformer  is  one  so  constructed 
that  the  relation  of  the  primary  and  the  secondary  voltage 
remains  practically  constant,  regardless  of  the  load  on  the 
transformer. 

The  constant-current  transformer  is  one  so  constructed  that 
the  secondary  current  remains  constant  in  value,  and  when 
the  load  on  the  transformer  changes,  there  is  a  change  in  the 
e.m.f.  induced  in  the  secondary  winding. 

The  current  transformer  is  one  so  constructed  that  the 
secondary  current  always  bears  a  definite  relation  to  the  pri- 
mary current.  These  transformers  are  used  principally  in 
connection  with  instruments  where  it  is  desired  to  send  a 
definite  fractional  part  of  the  total  line  current  through  the 
instrument.  They  correspond  to  the  shunt  in  the  direct- 
current  circuit. 

415.  The    Auto-Transformer. — The    auto-transformer    con- 
sists of  an  ordinary  transformer  with  its  primary  and   sec- 
ondary  coils   so  connected  with  respect  to   each   other  that 
the    e.m.f.    induced    in    the    secondary    coils    either    aids    or 
opposes  the  e.m.f.  impressed  upon  the  primary  coil.     When 
the  e.m.f.'s  of  the  two  windings  act  in  the   same   direction, 
it   is   said   to    be   an   auto-step-up    transformation,   and   when 
they  act  in  opposite  directions  it  is  said  to  be  an  auto-step- 
down  transformation. 

416.  Methods  of  Cooling  Transformers. — In  small-capacity 
transformers  the  radiating   surface   is   ample  to  prevent   an 
excessive  temperature  rise  when  the  transformer  is  in  opera- 
tion.    With  an  increase  in  capacity  of  the  transformer,  there 
is  a  proportional  increase  in  the  energy  loss,  and  hence  the 
heat  generated,  but  the  radiating  surface  does  not  increase  at 
the  same  rate  and,  as  a  result,  the  temperature  rise  will,  as 
a  rule,  be  greater  in  large  transformers  than  it  is  in  small 
ones,   unless    some    means    be    provided     for    cooling     them. 
Transformers  may  be  classified  according  to  the  method  em- 
ployed in  cooling  them  as  follows: 

(A)  Dry-transformers,  self-cooling. 

(B)  Oil-filled  transformers,  self-cooling. 


378 


PRACTICAL  APPLIED  ELECTRICITY 


(C)  Transformers  cooled  by  a  blast  of  air. 

(D)  Transformers  cooled   by  a  current  of  water. 

(E)  Transformers  cooled  by  a  combination  of  the  above. 

No  special  means  is  ever  employed  for  cooling  small  trans- 
formers, as  they  are  dry. 

Large  transformers  are  cooled  by  filling  the  space  sur- 
rounding the  coils  and  core  with  a  good  quality  of  oil,  which 
tends  to  equalize  the  temperature  of  the  vari6us  parts  and 
to  conduct  the  heat  to  the  containing  case  of  the  transformer, 
where  it  is  radiated.  The  containing  case  is  often  corrugated 
or  made  with  protruding  ribs,  which  adds  to  its  radiating  sur- 
face, as  shown  in  Fig.  316. 


Fig.  316 


Fig.  317 


Large  transformers  are  often  constructed  so  that  they  can 
be  cooled  by  forcing  a  blast  of  air  through  them.  The  coils 
in  such  transformers  are  usually  spread  apart  so  as  to  form 
ducts  through  which  the  air  may  circulate. 

Large  transformers  are  often  cooled  by  circulating  water 
through  a  pipe  which  surrounds  the  coils  and  core.  This 
method  of  cooling,  however,  is  usually  used  in  combination 
with  the  oil-cooled  type. 

417.  Rotating  Magnetic  Field. — Suppose  the  projecting 
arms  or  poles  on  the  field  frame  of  a  dynamo  be  divided  into 


THE  ALTERNATING-CURRENT  CIRCUIT  379 

three  groups,  and  the  poles  belonging  to  one  group  marked 
(Aj),  (A2),  (A;,),  etc.,  those  of  another  group  marked  (Bj), 
(B2),  (B3),  etc.,  and  the  third  group  (Ci),  (C2),  (C3),  etc., 
as  shown  in  Fig.  317.  If  a  winding  be  placed  on  the  poles 
belonging  to  any  group,  alternate  ones  being  wound  in  op- 
posite directions,  and  each  of  these  windings  then  connected 
to  a  source  of  direct  e.m.f.,  the  inner  end  of  the  poles  will 
be  magnetized  alternately  north  and  south.  If  an  alternating 
e.m.f.  be  used,  the  polarity  of  the  poles  belonging  to  any 
group  will  be  reversed  twice  per  cycle.  By  connecting  the 
three  groups  of  windings  to  the  different  phases  of  a  three- 
phase  circuit,  any  three  poles  that  occur  in  succession 
around  the  frame  will  not  be  magnetized  to  a  maximum 
polarity  of  the  same  time.  The  time  required  for  the  maximum 
polarity  to  pass  from  one  pole  to  the  next  is  one-third  of  a 
half  cycle  or  one-sixth  of  a  cycle.  The  maximum  polarity  is 
passed  from  one  pole  to  the  next  around  the  frame,  which 
results  in  what  is  termed  a  rotating  magnetic  field.  The  speed 
at  which  this  field  rotates  can  be  determined  as  follows:  Let 
(f)  represent  the  frequency  of  the  impressed  voltage,  (p) 
the  number  of  poles  per  phase,  and  since  two  poles  corre- 
spond to  one  cycle,  the  time  per  revolution  of  the  field  will 
be  equal  to 

2f 
time  per  revolution  =  —  (158) 

P 
and 

f 
number  of  revolutions  per  second  =  —  (159) 

2  P 

418.  Induction  Motor. — If  a  hollow  metal  cylinder  b€ 
mounted  inside  of  a  rotating  field,  there  will  be  an  e.m.f.  in- 
duced in  it,  due  to  the  relative  motion  of  the  field  and  the 
cylinder,  and  this  e.m.f.  will  produce  a  current  in  the  cylinder 
which  reacts  upon  the  magnetic  field  and  causes  the  cylinder 
to  rotate.  The  path  taken  by  the  induced  current  is  not 
very  well  defined  in  the  case  of  a  cylinder  and,  as  a  result,  it 
will  not  all  be  useful  in  producing  a  tangential  force.  This 
difficulty  is  overcome  by  slotting  the  cylinder  in  a  direction 
parallel  to  the  axis  about  which  it  rotates.  The  flux  passing 
between  poles  of  opposite  polarity  can  be  greatly  increased. 


380  PRACTICAL  APPLIED  ELECTRICITY 

with  the  same  current  in  the  winding,  by  mounting  the  cyl- 
inder upon  an  iron  core,  which  should  be  laminated.  This 
increase  in  flux  will  result  in  a  greater  e.m.f.  being  induced 
in  the  cylinder  and  a  greater  current  would  result,  which 
would  increase  the  force  tending  to  turn  the  cylinder.  The 
above  principles  are  those  upon  which  the  induction  motor 
operates. 


Fig.  318 


The  winding  of  an  induction  motor  that  is  stationary  is 
called  the  stator,  and  the  moving  part  is  called  the  rotor. 
The  stator  windings  are  usually  placed  in  slots  cut  in  what  is 
called  the  stator  core,  instead  of  being  wound  upon  poles  as 
shown  in  Fig.  317.  The  stator  core  of  a  small  induction  motor 
is  shown  in  Fig.  318.  The  rotor  in  its  simplest  form  consists 
of  copper  conductors  imbedded  in  slots  in  a  laminated  iron 
core.  These  conductors  are  all  connected  in  parallel  by  cop- 
per collars,  one  being  placed  at  each  end.  With  this  arrange- 
ment the  current  due  to  the  induced  e.m.f.  passes  in  a  direc- 
tion parallel  to  the  axis  about  which  the  rotor  rotates,  and 
its  effect  in  producing  rotation  is  a  maximum.  This  simple 
form  of  rotor  is  called  the  "squirrel-cage"  type,  Fig.  319.  The 
inductors  may  or  may  not  be  insulated  from  the  core. 


THE  ALTERNATING-CURRENT  CIRCUIT  381 

In  some  cases  the  rotor  is  provided  with  a  regular  wind- 
ing, and  this  winding  is  connected  to  an  external  circuit  by 
means  of  slip-rings. 

419.  Operation  of  the  Induction  Motor. — If  the  stator  be 
connected  to  a  source  of  energy  and  the  rotor  is  free  to  turn, 
it  will  run  at  such  a  speed  that  the  induced  e.m.f.  in  the 
rotor  winding  will  produce  the  current  required  to  drive  the 
rotor.  The  induced  e.m.f.  in  the  rotor  depends  upon  the  rela- 
tive movement  of  the  magnetic  field  and  the  rotor  winding. 


Fig.  319 


If  the  rotor  were  to  run  at  the  same  speed  that  the  magnetic 
field  revolves,  there  would  be  no  e.m.f.  induced  in  its  winding. 
Then  in  order  that  there  be  an  e.m.f.  induced  in  its  winding, 
its  speed  must  be  less  (in  the  case  of  a  motor)  than  that  of 
the  magnetic  field.  If  (Sf)  represents  the  speed  of  the  field, 
(SP)  the  speed  of  the  rotor,  then  the  fifference  in  speed  of 
the  rotor  and  the  magnetic  field  is  (Sf — SP).  This  difference 
in  speed  divided  by  (SP)  is  called  the  slip,  and  it  is  usually 
expressed  as  a  per  cent  of  the  synchronous  speed.  When  the 
motor  is  loaded,  the  rotor  speed  decreases  in  order  that  the 
current  may  increase  in  value,  it  depending  upon  the  induced 
e.m.f.,  which  in  turn  depends  upon  the  ratio  of  the  speeds  of 
the  rotor  and  the  magnetic  field.  A  three-phase  induction 
motor  is  shown  in  Fig.  320. 

420.  Speed  Regulation  of  the  Induction  Motor. — The  speed 
of  induction  motors  may  be  regulated  by  changing  the  value  of 
the  impressed  voltage  upon  the  stator,  by  changing  the  con- 
nections of  the  stator  winding  so  as  to  change  the  number 
of  poles,  or  by  changing  the  resistance  of  the  rotor  winding. 


382  PRACTICAL  APPLIED  ELECTRICITY 

With  a  decrease  in  impressed  voltage,  the  stator  flux  is 
lessened  and  the  rotor  current  decreases  if  the  speed  re- 
mains constant.  If  the  torque  the  motor  is  to  generate  is  to 
remain  constant,  it  being  proportional  to  the  product  of  the 
flux  and  the  rotor  current,  there  must  be  an  increase  in  rotor 
current  on  account  of  the  decrease  in  stator  flux,  in  order 
that  the  motor  carry  its  load.  The  required  increase  in  rotor 
current  is  produced  by  a  decrease  in  rotor  speed. 

If  the  stator  winding  be  changed,  so  as  to  change  the  num- 
ber of  poles,  there  will  be  a  corresponding  change  in  rotor 
speed,  the  slip  remaining  constant. 


Fig.  320 


If  the  resistance  of  the  rotor  be  increased,  the  e.m.f.  re- 
quired to  produce  a  given  rotor  current  must  increase,  and 
in  order  that  there  be  an  increase  in  rotor  e.m.f.  there  must 
be  a  decrease  in  rotor  speed. 

421.  Methods  of  Starting  the  Induction  Motor. — Polyphase 
induction  motors  may  be  started  by  connecting  their  stator 


THE  ALTERNATING-CURRENT  CIRCUIT  383 

windings  directly  to  the  line.  The  current  taken  from  the 
line,  however,  is  excessive,  and  an  auto-starter  or  com- 
pensator is  usually  used. 

Single-phase  induction  motors  will  not  start  when  their 
stator  windings  are  connected  to.  a  single-phase  circuit,  unless 
special  provision  is  made  for  starting.  There  are  four  meth- 
ods that  are  employed  for  starting  single-phase  motors,  viz, 

(A)  Hand  starting. 

(B)  Split-phase  starting. 

(C)  Repulsion  motor  starting. 

(D)  "Shading-coil"  starting. 


Fig.  321 

(A)  Very  small  induction  motors  may  be  started  by  giv- 
ing them  a  good  start  by  hand. 

(B)  In  split-phase  starting  there  are  two  circuits  through 
the  motor,  and  there  is  a  phase  difference  between  the  cur- 
rents in  the  two  branches,  if  the  ratio  between  the  resistance 
and  reactance  of  the  branches  is  different.     This  difference 
in  phase  of  the   currents   in  the  two   circuits   produces  the 
required   rotating  field   to   start    the    motor.     The    starting 


384  PRACTICAL  APPLIED  ELECTRICITY 

torque,  however,  is  very   small  when  the   current  does  not 
exceed  full-load  current. 

(C)  If   the    field    magnets    of   an    ordinary   direct-current 
dynamo  be  laminated  and  excited  by  an  alternating  current, 
there  would  be  induced  e.m.f.'s  set  up  in  the  armature  wind- 
ing, provided  the  brushes  were  changed  from  their  original 
position.      These    induced    e.m.f.'s    would    produce    currents 
which  would  react  upon  the  alternating  magnetic  field   and 
produce  a  torque  tending  to  cause  rotation.     A  single-phase 
alternating-current  motor  constructed  to  operate  in  the  above 
manner  is  called  a  repulsion  motor.    After  the  motor  is  up  to 
speed    the    brushes    are    automatically    disconnected    and    it 
operates  as  an  induction  motor. 

(D)  The  "shading-coil"  consists  of  a  single  turn  of  copper 
about  a  part  of  each  field-pole.     The  flux  through  the  part 
of  the   field-pole   enclosed   by  this   turn    of    wire    does    not 
change  in  value  as  rapidly  as  the  flux  in  the  remaining  por- 
tion of  the  pole,  due  to  the  magnetic  effect  of  the  current  in 
the  copper  coil  that  is  produced  by  the  e.m.f.  induced  in  it. 
As  a  result  of  the  above  condition  the  flux  travels  across  the 
pole-face  and  there  will  be  a  torque  exerted  upon  the  rotor. 

422.  Induction     Generator. — An     induction     motor     when 
operating  without  load  takes  a  very  small  current  from  the 
supply  leads  and  the  speed  of  its  rotor  is  very  near  that  of 
the  magnetic  field.    If  the  rotor  be  connected  to  some  source 
of  power  and  speeded  up  to  the  same  speed  as  that  of  the 
magnetic  field,  the  electrical  power  intake  of  the  stator  will 
be  very  small,  it  being  equal  to  the  iron  loss  in  the  stator. 
By  increasing  the  speed  of  the  rotor  until  it  is  above  syn- 
chronism,  the   stator   will   deliver   power  to   the   alternating- 
current  leads,  provided  the  alternating-current  generator  re- 
mains connected  to  the  leads  to  fix  the  frequency.    When  an 
induction  motor  is  so  used  it  is  called  an  induction  generator. 

423.  Frequency    Changer. — An    induction    motor    provided 
with  a  rotor  having  a  winding  with  terminals   connected  to 
collector  rings  may  be  used  as  a  frequency  changer,  that  is, 
it  may  be  used  to  change  the  frequency.     When  the  rotor  of 
the  motor  is  held  stationary,  the  magnetic  flux  of  the  stator 
induces  e.m.f.'s  in  the  rotor  winding  that  are  of  the  same 
frequency   as   the   alternating  e.m.f.'s   applied   to   the   stator. 
If  the  rotor  is  run  at  one-half  spe,ed,  in  the  direction  the  mag- 


THE  ALTEENATING-CUKRENT  CIECUIT  385 

netic  field  rotates,  the  e.m.f.'s  induced  in  the  rotor  windings 
will  be  one-half  full  frequency.  By  driving  the  rotor  in  the 
opposite  direction  to  the  direction  in  which  the  magnetic 
field  revolves,  the  frequency  is  raised.  Thus,  if  the  rotor  be 
revolved  backward  at  one-half  speed,  the  induced  e.m.f.'s  in 
the  rotor  windings  -will  be  one  and  one-half  times  the  fre- 
quency of  the  e.m.f.'s  impressed  upon  the  stator  windings. 

424.  Synchronous  Converter. — The  synchronous  converter 
is  a  machine  for  converting-  alternating-current  to  direct-cur- 
rent, or  vice  versa,  or  it  may  be  used  as  a  double-current  gen- 
erator. The  synchronous  converter  resembles  a  direct-cur- 
rent generator  in  general  appearance,  the  chief  difference 
being  the  addition  of  a  number  of  collector  rings  at  one  end 
of  the  armature,  and  the  use  of  a  larger  commutator  and 
smaller  magnetic  circuit  than  is  ordinarily  used  in  a  direct- 
current  generator. 

When  such  a  machine  is  driven  by  an  engine  or  motor,  it  is 
capable  of  supplying  either  direct  or  alternating  current,  or 
both  at  the  same  time.  It  may  be  driven  as  a  synchronous 
motor  from  an  alternating-current  source  of  energy  and  de- 
liver direct  current,  or  it  may  be  driven  from  a  direct-current 
source  of  energy  and  deliver  alternating  current. 

The  synchronous  converter  may  be  started  as  a  synchronous 
motor,  as  described  in  section  (406),  or  it  may  be  started  from 
the  direct-current  end.  In  starting  from  the  direct-current 
end,  the  machine  is  brought  up  to  a  speed  a  little  above  syn- 
chronous speed  and  then  disconnected  from  the  direct-current 
source,  and  when  the  speed  has  decreased  to  synchronous 
speed  the  alternating-current  end  is  connected  to  the  alternat- 
ing-current leads.  A  synchronous  converter  is  shown  in 
Fig.  321. 


CHAPTEE  XIX 

RESUSCITATION  FROM  APPARENT  DEATH  FROM 
ELECTRIC  SHOCK 

By  Augustin   H.  Goelet,   M.  D. 

Supplement  to  Electrical  World  and  Engineer,  September  6,  1902. 

425.  Resuscitation. — The  urgent  necessity  for  prompt  and 
persistent   efforts    at   resuscitation   of   victims   of   accidental 
shocks  by  electricity  is  very  well  emphasized  by  the  success- 
ful results  in  the  instances  recorded.     In  order  that  the  task 
may  not  be  undertaken  in  a  half-hearted  manner,  it  must  be 
appreciated  that  accidental  shocks  seldom  result  in  absolute 
death  unless  the  victim  is  left  unaided  too  long,  or  efforts  at 
resuscitation  are  stopped  too  early. 

In  the  majority  of  instances  the  shock  is  only  sufficient  to 
suspend  animation  temporarily,  owing  to  the  momentary  and 
imperfect  contact  of  the  conductors,  and  also  on  account  of 
the  resistance  of  the  body  submitted  to  the  influence  of  the 
current.  It  must  be  appreciated  also  that  the  body  under 
the  conditions  of  accidental  shocks  seldom  receives  the  full 
force  of  the  current  in  the  circuit,  but  only  a  shunt  current, 
which  may  represent  a  very  insignificant  part  of  the  whole. 

When  an  accident  occurs  the  following  rules  should  be 
promptly  executed  with  care  and  deliberation: 

426.  Rule  (1) — Remove  the  body  at  once  from  the  circuit  by 
breaking    contact    with    the    conductors.      This    may    be    ac- 
complished  by  using  a  dry  stick  of  wood,  which  is  a  non- 
conductor, to  roll  the  body  over  to  one  side,  or  to  brush  aside 
a  wire,  if  that  is  conveying  the  current.    When  a  stick  is  not 
at  hand,  any  dry  piece  of  clothing  may  be  utilized  to  protect 
the  hand  in   seizing  the  body  of  the  victim,  unless  rubber 
gloves   are   convenient.     If  the   body  is   in  contact  with  the 
earth,  the  coat-tails  of  the  victim,  or  any  loose  or  detached 


RESUSCITATION 


387 


piece  of  clothing  may  be  seized  with  impunity  to  draw  it 
away  from  the  conductor.  When  this  has  been  accomplished, 
observe  Rule  (2).  The  object  to  be  attained  is  to  make  the 
subject  breathe,  and  if  this  can  be  accomplished  and  con- 
tinued he  can  be  saved. 

427.     Rule   (2) — Turn  the  body  upon  the  back,  loosen  the 
collar  and  clothing  about  the  neck,  roll  up  a  coat  and  place  it 


Fig.  322 

under  the  shoulders,  so  as  to  throw  the  head  back,  and  then 
make  efforts  to  establish  respiration  (in  other  words,  make 
him  breathe),  just  as  would  be  done  in  case  of  drowning.  To 
accomplish  this,  kneel  at  the  subject's  head,  facing  him  as 
shown  in  Fig.  322,  and,  seizing  both  arms,  draw  them  forcibly 
to  their  full  length  over  the  head,  so  as  to  bring  them  almost 
together  above  it,  and  hold  them  there  for  two  or  three  sec- 
onds only.  (This  is  to  expand  the  chest  and  favor  the  en- 
trance of  air  into  the  lungs.)  Then  carry  the  arms  down  to 
the  sides  and  front  of  the  chest,  firmly  compressing  the  chest 
walls,  and  expel  the  air  from  the  lungs,  as  shown  in  Fig.  323. 
Repeat  this  manoeuvre  at  least  sixteen  times  per  minute. 
These  efforts  should  bo  continued  unremittingly  for  at  least 
an  hour,  or  until  natural  respiration  is  established. 

428.  Rule  (3) — At  the  same  time  that  this  is  being  done, 
someone  should  grasp  the  tongue  of  the  subject  with  a 
handkerchief  or  piece  of  cloth,  to  prevent  it  slipping,  and 


388 


PRACTICAL  APPLIED  ELECTRICITY 


draw  it  forcibly  out  when  the  arms  are  extended  above  the 
head  and  allow  it  to  recede  when  the  chest  is  compressed. 
This  manoeuver  should  likewise  be  repeated  at  least  sixteen 
times  per  minute.  This  serves  the  double  purpose  of  free- 
ing the  throat  so  as  to  permit  air  to  enter  the  lungs,  and 
also,  by  exciting  a  reflex  irritation  from  forcible  contact  of 
the  under  part  of  the  tongue  against  the  lower  teeth,  fre- 
quently stimulates  an  involuntary  effort  at  respiration.  To 
secure  the  tongue  if  the  teeth  are  clenched,  force  the  jaws 


Fig.   323 


apart  with  a  stick,  a  piece  of  wood,  or  the  handle  of  a  pocket 
knife. 

429.  Rule  (4) — The  dashing  of  cold  water  into  the  face 
will  sometimes  produce  a  gasp  and  start  breathing,  which 
should  then  be  continued  as  directed  above.  If  this  is  not 
essential  the  spine  may  be  rubbed  vigorously  with  a  piece  of 
ice.  Alternate  applications  of  heat  and  cold  over  the  region 
of  the  heart  will  accomplish  the  same  object  in  some  in- 
stances. It  is  both  useless  and  unwise  to  attempt  to  ad- 
minister stimulants  to  the  victim  in  the  usual  manner  of 
pouring  it  down  his  throat. 

While  the  above  directions  are  being  carried  out,  a  physi- 
cian should  be  summoned,  who,  upon  his  arrival,  can  best  put 
into  practice  Rules  (5),  (6)  and  (7),  in  addition  to  the  fore- 
going, should  it  be  necessary. 


RESUSCITATION  389 

FOR  THE  PHYSICIAN   SUMMONED 

430.  Rule  (5) — Forcible  stretching  of  the  sphincter  muscle 
controlling  the  lower  bowel  excites  powerful  refle::  irritation 
and   stimulates   a   gasp    (inspiration)    frequently  when   other 
measures  have  failed.    For  this  purpose  the  subject  should  be 
turned   on  the   side,   the  middle   and   index  fingers   inserted 
into  the  rectum,  and  the  muscle  suddenly  and  forcibly  drawn 
backwards  toward  the  spine.    Or,  if  it  is  desirable  to  continue 
efforts  at  artificial  respiration  at  the  same  time,  the  knees 
should  be  drawn  up  and  the  thumb  inserted  for  the  same 
purpose,  the  subject  retaining  the  position  on  the  back. 

431.  Rule  (6) — Rhythmical  traction  of  the  tongue  is  some- 
times effectual  in  establishing  respiration  when  other  meas- 
ures have  failed.    The  tongue  is  seized  and  drawn  out  quickly 
and  forcibly  to  the  limit,  then  it  is  permitted  to  recede.    This 
is  to  be  repeated  16  times  per  minute. 

432.  Rule  (7) — Oxygen  gas,  which  may  be  readily  obtained 
at  a  drug  store  in  cities  or  large  towns,  is  a  powerful  stimu- 
lant to  the  heart  if  it  can  be  made  to  enter  the  lungs.     A 
cone  may  be  improvised  from  a  piece  of  stiff  paper  and  at- 
tached to  the  tube  leading  from  the  tank,  and  placed  over  the 
mouth  and  nose  while  the  gas  is  turned  on  during  the  efforts 
at  artificial  respiration, 


CHAPTEE  XX 

LOGARITHMS 

433.  Definition  of  Logarithm. — If  (a)  be  any  number,  and 
(x)  and   (n)  two  other  numbers,  such  that  ax  =  n,  then   (x) 
is  called  the  logarithm  of  (n)  to  the  base  (a)  and  is  written 
logan.     The  logarithm  of  a  number  to  a  given  base  is  the 
index  of  the  power  to  which  the  base  must  be  raised  that  it 
may  be  equal  to  the  given  number.     Example:    Since  102  = 
100,  therefore  2  =log10100. 

434.  Laws    of    Indices. — In    algebra    the    following    laws, 
known  as  the  laws  of  indices,  are  found  to  be  true;   (m)  and 
(n)  are  to  be  any  real  quantities: 

(A)  amXan  =  am  +  n 

(B)  am  -=-  an  =  am  —  n 

(C)  (am)n  =  ara  X  n 

There  are  three  fundamental  laws  of  logarithms  correspond- 
ing to  the  above. 

(a)  loga  (m  X  n)  =  logam  +  logan 

(b)  loga    (m  -T-  n)  =  logam  —  logan 

(c)  logam.n  =  n  logam. 
These  three  laws  expressed  in  words  are: 

(a)  The   logarithm   of  the   product   of   two   quantities   is 
equal  to  the  sum  of  the  logarithms  of  the  quantities  to  the 
same  base. 

(b)  The   logarithm  of  the   quotient  of   two   quantities   is 
equal  to  the  difference  in  their  logarithms  to  the  same  base. 

(c)  The  logarithm  of  a  quantity  raised  to  any  power  is 
equal  to  the  logarithm  of  the  quantity  multiplied  by  the  index 
of  the  power. 

435.  Common   System   of   Logarithms. — In  what  is  known 
as  the  common  system  of  logarithms  the  base  is  always  10, 
so  that  if  no  base  be  expressed,  the  base  10  is  always  under- 
stood. 

390 


LOGARITHMS  391 

436.  Definition    of    Characteristic    and     Mantissa. — If    the 
logarithm  of  any  number  be  partly  integral  and  partly  frac- 
tional, the  integral  portion  is  called  its  characteristic  and  the 
decimal  portion  is  called  its  mantissa.     Thus,  the  logarithm 
of    666    is    2.82347,    in    which    2    is    the    characteristic    and 
.82347  is  the  mantissa. 

The  characteristic  of  the  logarithm  of  any  whole  number 
will  be  one  less  than  the  number  of  digits  in  its  integral  part. 
Thus,  2457.4  has  four  digits  in  its  integral  part  and  the  char- 
acteristic of  its  logarithm  is  3. 

The  characteristic  of  the  logarithm  of  any  decimal  frac- 
tion will  be  negative  and  numerically  greater  by  unity  than 
the  number  of  ciphers  following  the  decimal  point.  Thus, 
.897  has  no  ciphers  following  the  decimal  point  and  the  char- 
acteristic will  be  numerically  equal  to  (0  +  1)  or  1,  and  it 
will  be  negative.  The  fact  that  the  characteristic  is  negative 
can  be  indicated  by  drawing  a  horizontal  line  over  it,  thus 
(1).  The  characteristic  of  .00434  is  "3  since  there  are  two 
ciphers  following  the  decimal  point. 

The  mantissa  of  the  logarithm  of  all  numbers  consisting 
of  the  same  digits  are  the  same. 

437.  How   to    Obtain    the    Logarithm    of   a    Number    from 
the   Table. — For   example,    if    it    is    desired     to     obtain     the 
logarithm  of  the  number  642,  we  proceed  as  follows:     Run 
the  eye  down  the  extreme  left-hand  column  until  it  arrives 
at  the  number  64.     Then  pass  along  the  horizontal  line  of 
figures  until  you  are  in  the  column  vertically  beneath  the 
number  2  at  the  top  of  the  page,  and  you  see  the  number 
80754.     This   number  just  obtained   is   the   mantissa   of  the 
log  of  642  and  the  characteristic  is  2. 

Then  log     642  =*  2.807  54 

and  log  6420  =  3.807  54 

log    6.42=    .80754 

log  .00642  =  3.80754 

438.  To  Find  a  Number  Whose  Logarithm  Is  Given. — If  the 

logarithm  be  one  tabulated  in  the  table  the  number  is  easily 
found,  the  procedure  being  just  the  reverse  of  that  given  in 
the  previous  paragraph.  Example:  Find  the  number  whose 
logarithm  is  68931.  Referring  to  the  table,  we  find  the 


392  PRACTICAL  APPLIED  ELECTRICITY 

mantissa  68931  corresponds  to  the  digits  489,  and  the  number 
will  be  4890,  since  the  characteristic  is  3. 

Often  the  logarithm  is  not  tabulated  and  the  number  is 
then  found  as  follows:  Example — Find  the  number  whose 
logarithm  is  3.44741.  Referring  to  the  table,  we  find  that  the 
mantissa  44741  is  not  tabulated,  but  the  nearest  mantissae 
are  44716  and  44871,  between  which  the  mantissa  44741  lies. 
The  difference  between  44871  and  44716  is  155,  and  the  differ- 
ence between  44741  and  44716  is  75. 

log  2800  =  3.447  16 

log  2810  =  3.448  71 
then  3.447  41  =  log  (2800  +  X) 

75 
X  = of  10  =  4.99 

155 

The  required  number  then  is  (2800  +  4.99)  =  2804.99. 


EXAMPLES 

(A)     What  is  the  value  of  the  product  of  24  and  19? 
log  24  =  1.380  21 
log  19  =  1.278  75 


log  (product)  =  2.658  96 
then  (24  X  19)  =  456 

(B)  What  is  the  value  of  (27)2? 

log  (27)2  =  2  log  27 
=  2.862  72 
then  (27)2  =  729 

(C)  What  is  the  value  of  the  product  of  .079  and  .03? 

log  .079  =  27897  63 
log  .03    ==2L47712 


log  (product)  =  3.374  75     (See  note  a,  pa?e 
then  (.079  X  .03)  =    .002  37  393) 


LOGARITHMS  393 

(D)     What  is  the  value  of  the  product  of  .65  and  48? 

log.65=T.81291 
log  48  =  1.681  24 


log  (product)  =  1.494  15 
then  (.65  X  48)  =  31.25 

(E)  What  is  the  value  of  (.075)2? 

log  .075  =  "2T875  06 

2  log  .075  =  "3.750  12 

then   (.075)2=  .005  625 

(F)  What  is  the  value  of  (79.0)1-6? 

log  79.0  =  1.897  63 
log  (79.0)1-6  =  1.6  X  1.89763 

=  2.936  208 
then  (79.0)1-6  =  863.+ 


(G)     What  is  the  value  of  V  656100     ? 

log  656100  =  5.816  90 

%  log  656100  =  2.908  45 

or  log  V  656100  =  2.908  45 

then  V  656100  =  810 

Note  (a) — The  characteristic  is  treated  as  a  negative  quan- 
tity and  the  mantissa  as  a  positive  quantity. 


394 


LOGABITHMS  OF  NUMBERS 


No.          0             1             23456 

7 

8            9 

0 

00000 

041  39 
32222 
49136 
61278 
70757 
78533 
85126 
90849 
95904 

30103 

07918 
34242 
505  15 
62325 
71600 
79239 
85733 
91381 
96379 

47712 

11394 
361  73 
51851 
63347 
72428 
79934 
86332 
91908 
96848 

60206 

14613 
38021 
53148 
64345 
73239 
806  18 
86923 
92428 
97313 

69897 

17609 
39794 
544  07 
65321 
74036 
81291 
87506 
92942 
97772 

77815 

84510 

903  09    954  24 

1 
2 
3 
4 
5 
6 
7 
8 
9 

00000 
30103 
477  12 
60206 
69897 
77815 
845  10 
90309 
95424 

20412 
41497 
55630 
66276 
74819 
81954 
88081 
93450 
98227 

23045 
43136 
56820 
67210 
75587 
82607 
88649 
93952 
98677 

25527    27875 
447  16    462  40 
579  78    591  06 
681  24    690  20 
763  43    770  85 
832  51     818  85 
892  09    897  63 
944  48    949  39 
991  23  |  995  64 

10 

00000 

00432 

00860 

01284 

01703 

021  19 

02531 

02938 

03342    03743 

11 
12 
13 
14 
15 
16 
17 
18 
19 

20 

04139 
07918 
11394 
14613 
17609 
204  12 
23045 
25527 
27875 

04532 
08279 
11727 
14922 
17898 
20683 
23300 
25768 
28103 

04922 
08636 
12057 
15229 
18184 
20952 
23553 
26007 
28330 

05308 
08991 
12385 
15534 
18469 
21219 
23805 
26245 
28556 

05690 
09342 
127  10 
15836 
18752 
21484 
24055 
26482 
28780 

06070 
09691 
13033 
16137 
19033 
21748 
24304 
267  17 
29003 

06446 
10037 
13354 
16435 
193  12 
22011 
24551 
26951 
29226 

06819 
10380 
13672 
16732 
195  90 
22272 
24797 
271  84 
29448 

07188 
10721 
13988 
17026 
19866 
22531 
25042 
27416 
29667 

07555 
11059 
14301 
17319 
20140 
22789 
25285 
27646 
29885 

30103 

30320 

30535 

307  50 

30963 

31175 

31387 

31597 

31806    32015 

21 
22 

23 
24 
25 
26 

27 
28 
29 

32222 
34242 
361  73 
38021 
39794 
41497 
43136 
44716 
46240 

47712 

32428 
34439 
36361 
38202 
39967 
41664 
43297 
44871 
46389 

32634 
34635 
36549 
38382 
40140 
41830 
43457 
45035 
46538 

32838 
34830 
36736 
38561 
40312 
41996 
436  16 
45179 
46687 

33041 
35025 
36922 
38739 
40483 
42160 
43775 
45332 
46835 

33244 
35218 
37107 
38917 
40654 
42325 
43933 
45484 
46982 

33445 
354  11 
37291 
39094 
40824 
42488 
44091 
45637 
47129 

33646 
35603 
37475 
39270 
40993 
42651 
44248 
45788 
47276 

33846 
35793 
37658 
39445 
41162 
42813 
44404 
45939 
47422 

34044 
35984 
37840 
39620 
41330 
42975 
44560 
46090 
47567 

30 

47857 

48001 

48144 

48287 

48430 

48572 

48714 

48855 

48996 

31 
32 
33 
34 
35 
36 
37 
38 
39 

49136 
505  15 
51851 
53148 
54407 
55630 
56820 
57978 
59106 

49276 
50651 
51983 
53275 
54531 
55751 
56937 
58092 
59218 

49415 
50786 
521  14 
53403 
54654 
55871 
57054 
58206 
59329 

49554 
50920 
52244 
53529 
54777 
55991 
57171 
583  20 
59439 

49693 
51055 
52375 
53656 
54900 
561  10 
57287 
58433 
59550 

60638 

49831 
51188 
52504 
537  82 
55023 
56229 
57403 
58546 
59660 

60746 

49969 
51322 
52634 
53908 
551  45 
56348 
575  19 
58659 
59770 

60853 

50106 
51455 
52763 
54033 
55267 
56467 
57634 
58771 
59879 

50243 
51587 
52892 
54158 
55388 
56585 
57749 
58883 
59988 

50379 
51720 
53020 
54283 
55509 
56703 
57864 
58995 
60097 

40 

60206 

603  14    604  23 

60531 

60959 

61066 

61172 

41 
42 
43 
44 
45 
46 
47 
48 
49 

61278 
62325 
63347 
64345 
65321 
66276 
67210 
68124 
69020 

61384 
624  28  , 
63448 
64444 
65418 
66370 
67302 
682  15 
69108 

61490 
62531 
63548 
64542 
65514 
66464 
67394 
68305 
69197 

61595 
62634 
63649 
64640 
65610 
66558 
67486 
68395 
69285 

61700 
62737 
63749 
64738 
65706 
66652 
67578 
68485 
69373 

61805 
62839 
63849 
64836 
65801 
66745 
67669 
68574 
69461 

70329 

61909 
62941 
63949 
64933 
65896 
66839 
67761 
68664 
69548 

62014 
63043 
64048 
65031 
65992 
66932 
67852 
68753 
69636 

621  18 
63144 
64147 
65128 
66087 
67025 
67943 
68842 
69723 

62221 
63246 
64246 
65225 
66181 
67117 
68034 
68931 
69810 

50 

69897 

69984 

70070 

70157 

70243 

70415 

70501 

70586 

70672 

LOGARITHMS  OF  NUMBERS 


395 


No. 

0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

51 
52 
53 
54 
55 
56 
57 
58 
59 

70757 
71600 
72428 
73239 
74036 
748  19 
75587 
76343 
77085 

70842 
71684 
72509 
73320 
741  15 
74896 
75664 
76418 
77159 

70927 
71767 
72591 
73400 
74194 
74974 
75740 
76492 
77232 

71012 
71850 
72673 
73480 
74273 
75051 
75815 
76567 
77305 

71096 
71933 
72754 
73560 
74351 
751  28 
75891 
76641 
77379 

71181 
720  16 
72835 
73640 
74429 
75205 
75967 
76716 
77452 

71265 
72099 
72916 
73719 
74507 
75282 
76042 
76790 
77525 

71249 
72181 
72997 
73799 
74586 
75358 
76118 
76864 
77597 

71433 
72263 
730  .78 
73878 
74663 
75435 
76193 
76938 
77670 

71517 
723  46 
73159 
73957 
74741 
75511 
76268 
77012 
77743 

60 

77815 

77887 

77960 

78032 

78104 

78176 

78247 

78319 

78390 

78462 

61 
62 
63 
64 
65 
66 
67 
68 
69 

785  33 
79239 
79934 
80618 
81291 
81954 
82607 
83251 
83885 

78604 
79309 
80003 
80686 
81358 
82020 
82372 
833  15 
83948 

78675 
79379 
80072 
80754 
81425 
82086 
82737 
83378 
84011 

78746 
79449 
80140 
80821 
81491 
82151 
82802 
834  42 
840  73 

78817 
795  18 
80209 
80889 
81558 
82217 
82866 
83506 
841  36 

78888 
79588 
80277 
80956 
81624 
82282 
82930 
83569 
841  98 

78958 
79657 
80346 
81023 
81690 
823  47 
82995 
83632 
84261 

79029 
79727 
80414 
81090 
81757 
82413 
83059 
83696 
84323 

79099 
79796 
80482 
81158 
81823 
82478 
83123 
83759 
84386 

79169 
79865 
80550 
81224 
81889 
82543 
83187 
83822 
84448 

70 

84510 

84572 

84634 

84696 

84757 

848  19 

84880 

84942 

85003 

85065 

71 
72 
73 
74 
75 
76 
77 
78 
79 

85126 
85733 
863  32 
86923 
87506 
88081 
88649 
89209 
89763 

85187 
85794 
863  92 
86982 
87364 
88138 
887  05 
89263 
89919 

85248 
85854 
86451 
87040 
87622 
88195 
88762 
89321 
89873 

85309 
859  14 
86510 
87099 
87679 
88252 
888  18 
89376 
89927 

85370 
85974 
86570 
87157 
87737 
88319 
88874 
89432 
89982 

85431 
86034 
86629 
872  16 
87795 
88366 
88930 
89487 
90037 

85491 
86094 
86688 
87274 
87852 
88423 
88986 
89542 
90091 

85552 
86153 
86747 
87332 
87910 
88480 
89042 
89597 
90146 

85612 
86213 
86806 
87390 
87967 
88536 
89098 
89653 
90200 

85673 
86273 
86864 
87448 
88024 
88593 
89154 
89708 
90255 

80 

90309 

90363 

90417 

90472 

90526 

90580 

906  34 

90687 

90741 

90795 

81 
82 
83 
84 
85 
86 
87 
88 
89 

90849 
91381 
91908 
92428 
92942 
93450 
93952 
94448 
94939 

90902 
914  34 
91960 
92480 
92993 
935  00 
94002 
94498 
94988 

90956 
91487 
92012 
92531 
93044 
93551 
94052 
94547 
95036 

91009 
91540 
92065 
92583 
93095 
93601 
94101 
94596 
95085 

91062 
91593 
921  17 
92634 
93146 
93651 
94151 
94645 
95134 

91116 
91645 
92169 
92686 
93197 
93702 
94201 
94694 
95182 

91169 
91698 
92221 
92737 
93247 
93752 
94250 
94743 
95231 

91222 
91751 
92273 
92788 
93298 
93802 
94300 
94792 
95279 

91275 
91803 
92324 
92840 
93349 
93852 
94349 
94841 
95328 

91328 
91855 
92376 
92891 
93399 
93902 
94399 
94890 
95376 

90 

95424 

95472 

955  21 

95569 

956  17 

95665 

95713 

95761 

95809 

95856 

91 
92 
93 
94 
95 
96 
97 
98 
99 

95904 
96379 
96348 
973  13 
97772 
98227 
98677 
99123 
99564 

95952 
96426 
96895 
973  59 
97814 
98272 
98722 
99167 
99607 

95999 
96473 
96942 
97405 
97864 
98318 
98767 
99211 
99651 

96047 
96520 
96988 
97451 
97909 
98363 
98811 
99255 
99695 

96095 
96567 
97035 
97497 
979  55 
98408 
98856 
99300 
99739 

961  42 
96614 
97081 
97543 
98000 
98453 
98900 
99344 
99782 

96190 
96661 
97128 
97589 
98046 
98498 
989  45 
99388 
99826 

96237 
96708 
97174 
97635 
98091 
98543 
98989 
99432 
99870 

96284 
96755 
97220 
97681 
98137 
98588 
99034 
994  76 
99913 

96332 
96802 
97267 
97727 
98182 
98632 
99078 
99520 
99957 

100 

00000 

00043 

00087 

00130 

00173 

00217 

00260 

00303 

00346 

00389 

196 


MENSUBATION  EQUATIONS 


TRIGONOMETRICAL  FUNCTIONS 


j2"xX^ 


a       5inee=-^-     Cosinee=Y  Tangent  e=~t" 


Base  =  b 

Altitude  =  a 

Hypothe_nuse=h 

b^a2  +  b2 


MENSURATION 


Diameter 


Circumference 
TT=  3.1416- 

=  TTxr2 
xn  xd2 


Length  =1 

Breath  -b 

Depth  =  d 

Volu7ne=lxbxd 

Area  surface= 


Area  Shaded 
Portion^  (dj-dj) 


l=b  =  d 
Volume  =lx  b  xd 


Area   Shaded 
/2[lr-C(r-h)] 


Surface 


TRIGONOMETRICAL  FUNCTIONS 


397 


NATURAL  SINES,  COSINES,  AND  TANGENTS 


An- 
gle 

Sines 

Cosines 

Tangents 

An- 
gle 

Sines 

Cosines 

Tangents 

0 

.000000 

1.000000 

.000000 

46 

.719  340 

.694658 

.0355303 

1 

.017  452 

.999  848 

.017  455 

47 

.731  354 

.681  998 

.072  368  7 

2 

.034899 

.999  391 

.034921 

48 

.743  145 

.669  131 

.1106125 

3 

.052  336 

.998  630 

.02  408 

49 

.754  710 

.656  059 

.1503684 

4 

.069  756 

.997  564 

.069  927 

50 

.766044 

.642788 

1.1917536 

5 

.087  156 

.996  165 

.087  489 

51 

.777  146 

.629  320 

.234  897  2 

6 

.104528 

.994522 

.105  104 

52 

.788  Oil 

.615  661 

.279  941  6 

7 

.121869 

.992  546 

.122785 

53 

.798  636 

.601  815 

.3270448 

8 

.139173 

.990268 

.140541 

54 

.809017 

.587785 

1.3763810 

9 

.156434 

.987  688 

.158384 

55 

.819  152 

.573  576 

1.4281480 

10 

.173648 

.984808 

.176327 

56 

.829  038 

.559  193 

1.4825610 

11 

.  190  809 

.981  627 

.194380 

57 

.838  671 

.544639 

1.5398650 

12 

.207  912 

.978  148 

.212  557 

58 

.848048 

.529919 

1.6003345 

13 

.224951 

.974370 

.230  868 

59 

.857  167 

.515038 

1.6642795 

14 

.241  922 

.970296 

.249  328 

60 

.866  025 

.500000 

1.7320508 

15 

.258  819 

.965  926 

.267  949 

61 

.874  620 

.484  810 

1.8040478 

16 

.275  637 

.961  262 

.286  745 

62 

.882  948 

.469472 

1.8807265 

17 

.292372 

.956  305 

.305  731 

63 

.891  007 

.453  990 

1.9626105 

18 

.309  017 

.951  057 

.324  920 

64 

.898794 

.438  371 

2.0503038 

19 

.325  568 

.945  519 

.344  328 

65 

.906  308 

.422618 

2.1445069 

20 

.342020 

.939693 

.363  970 

66 

.913  545 

.406737 

2.2460368 

21 

.358368 

.933  580 

.383  864 

67 

.920  505 

.390  731 

2.3558524 

22 

.374607 

.927  184 

.404  026 

68 

.927  184 

.374607 

2.4750869 

23 

.390  731 

.920  505 

.424  475 

69 

.933  580 

.358  369 

2.6050891 

24 

.406  737 

.913545 

.445  229 

70 

.939  693 

.342  020 

2.7474774 

25 

.422  618 

.906  308 

.466  308 

71 

.945  519 

.325  568 

2.9042109 

26 

.438  371 

.898794 

.487  733 

72 

.951  057 

.309  017 

3.0776835 

27 

.453  990 

.891  007 

.509525 

73 

.956  305 

.292  372 

3.2708526 

28 

.469472 

.882  948 

.531  709 

74 

.961  262 

.275  637 

3.4874144 

29 

.484810 

.874  620 

.554  309 

75 

.965  926 

.258  819 

3.7320508 

30 

.500000 

.866025 

.577  350 

76 

.970  296 

.241  922 

4.0107809 

31 

.515  038 

.857  167 

.600861 

77 

.974  370 

.224  951 

4.3314759 

32 

.529  919 

.848048 

.624  869 

78 

.978  148 

.207  912 

4.7047301 

33 

.544  639 

.838671 

.649  408 

79 

.981  627 

.190809 

5.1445540 

34 

.559  193 

.829  038 

.674  509 

80 

.984  808 

.173648 

5.6712818 

35 

.573  576 

.819  152 

.700  208 

81 

.987  688 

.156434 

6.313  751  5 

36 

.587  785 

.809017 

.726  543 

82 

.990  268 

.139173 

7.1153697 

37 

.601  815 

.798636 

.753  554 

83 

.992  546 

.121869 

8.1443464 

38 

.615  661 

.788011 

.781  286 

84 

.994  522 

.104528 

9.5143645 

39 

.629320 

.777  146 

.809  784 

85 

.996  195 

.087  156 

11.430052 

40 

.642  788 

.766044 

.839  100 

86 

.997  564 

.069756 

14.300666 

41 

.656059 

.754710 

.869  287 

87 

.998  630 

.052  336 

19.081  137 

42 

.669  131 

.743  145 

.900  404 

88 

.999  391 

.034899 

28.636253 

43 

.681  998 

.731  354 

.932  515 

89 

.999  848 

.017  452 

57.289962 

44 

.694  658 

.719340 

.965  689 

90 

1.000000 

.000000 

infinite 

45 

.707  107 

.707  170 

1.000000 

398 


SYMBOLS  FOE  ELECTEICAL  APPAKATUS 


Wire 


Wires  not 
Connected 


Wires 
Connected 


Ground 
Connection 

Fuse 

—  -MA/W  — 

Non-Inductive 
Resistance 


PrfmaryCell 


Double-Pole  Double 
Throw  Switch  (Open) 


Ammeter 


V 


Voltmeter 


Galvanometer 


Direct-Current 
Generator 


Direct-Current 
Motor 


Load 


006 


W 


Wattmeter 


Inductive 
Resistance 

—  WWVi  - 

Variable 

Resistance  or 

Rheostat 


Incandescent 
Lamps  in  Series 

X — X — X— X— 

Arc  Lamps 
in  Series 


Alternating- 
Current  Generator 

'/ffTOWs 


Simple  Switch  Transformer 


Single-Pole  Single 
Throw  Switch  (Open) 


Condenser 


Single-Pole  Double         

'Throw  Switch  (Open)      Deta  Connection 


Double-Pole  Single-        

Throw  Switch  (Open)      Star  Connection 


TABLE  A 


399 


RELATION  OF  METRIC  AND  ENGLISH  MEASURES 
Equivalents  of  Linear  Measures 


Millimeter  
Centimeter  
Decimeter  
Meter  
Decameter  
Hectometer  
Kilometer  

Meters 

English  Measures 

Inches 

Feet 

Yards 

Miles 

.000621 
.006214 
.062  138 
.621  382 

.001 
.01 
.1 
1. 
10. 
100. 
1000. 

.039  371 
3.937079 
.328089 
39.370790 

.003  281 
.032  809 
.328089 
3.280899 
32.80899 
328.0899 
3280.899 

.001  094 
.010936 
.  109  363 
1.093633 
10.936  33 
109.3633 
1093.633 

English  Measures 

Meters 

Reciprocals 

.02539954 

39.37079 

12  inches  —  1  foot                                                    •           

.3047945 

3.280899 

3  feet  —  1  vard  

.9143835 

1.093633 

Equivalents  of  Surface  Measures 


Square 
Meters 

English  Measures 

Square 
inches 

Square 
feet 

Square 
yards 

Milliare  

.1 
1. 
10. 
100. 
1000. 
10000. 
1000000. 

155.01 
1550.06 
15500.59 
155005.9 

1.076 
10.764 
107.64 
1076.4 
10764.3 
107643. 

.119 
1.196 
11.960 
119.6033 
1096.033 
11960.33 

Diciare  

Decare  (not  used)  
Hectare  
Square  Kilometer  

English  Measures 

Metric  Measures 

Reciprocals 

6.451367     sq.  cmt. 

.  1550059 

144  sq  in  —  1  sq  ft 

09289968  sq.    m. 

10.7642996 

9  sq.  ft.=l  sq.  yd  

.8360972    sq.    m. 

1.196033 

Equivalents  of  Weights 


Grams 

English  Weights 

Oz. 
avoir 

Lbs. 
avoir 

Tons 
2000  Ibs. 

Tons 
2240  Ibs. 

Milligram  
Centigram  
Decigram  

.001 
.01 
.1 
1. 
10. 
100. 
1000. 

.0353 
.3527 
3.5274 
35.2739 

.0022 
.02205 
.22046 
2.2046 

.001102 

.000984 

Gram  

Hectogram  
Kilogram  

English  Weights  "Avoirdupois" 

Grams 

Reciprocals 

.06479895 

15.43234875 

1  771836 

.564383 

16  drams=l  oz.=437  .  5  grains  
16  oz.l  rjound==7000  grains  

28.349375 
453.592652 

.0352739 
.00220462 

400 


TABLE  B 


TABLE  OF  COMPARISON  OF  CENTIGRADE  AND  FAHRENHEIT 
THERMOMETER  SCALES 


Cent, 

Fahr. 

Cent. 

Fahr. 

Cent. 

Fahr. 

Cent. 

Fahr. 

0 

32.0 

26 

78.8 

51 

123.8 

76 

168.8 

1 

33.8 

27 

80.6 

52 

125.6 

77 

170.6 

2 

35.6 

28 

82.4 

53 

127.4 

78 

172.4 

3 

37.4 

29 

84.2 

54 

129  2 

79 

179.2 

4 

39.2 

30 

86.0 

55 

131.0 

80 

176.0 

5 

41.0 

31 

87.8 

56 

132.8 

81 

177.8 

6 

42.8 

32 

89.6 

57 

134.6 

82 

179.6 

7 

44.6 

33 

91.4 

58 

136.4 

83 

181.2 

8 

46.4 

34 

93.2 

59 

138.2 

84 

183.4 

9 

48.2 

35 

95.0 

60 

140.0 

85 

185.0 

10 

50.0 

36 

96.8 

61 

141.8 

86 

186.8 

11 

51.8 

37 

98.6 

62 

143.6 

87 

188.6 

12 

53.6 

38 

100.4 

63 

145.4 

88 

190.4 

13 

55.4 

39 

102.2 

64 

147.2 

89 

192.2 

14 

57.2 

40 

104.0 

65 

149.0 

90 

194.0 

15 

59.0 

41 

105.8 

66 

150.8 

91 

195.8 

16 

60.8 

42 

107.6 

67 

152.6 

92 

197.6 

17 

62.6 

43 

109.4 

68 

154.4 

93 

199.4 

18 

64.4 

44 

111.2 

69 

156.2 

94 

201.2 

19 

66.2 

45 

113.0 

70 

158.0 

95 

203.0 

20 

68.0 

46 

114.8 

71 

159.8 

96 

204.8 

21 

69.8 

47 

116.6 

72 

161.6 

97 

206.6 

22 

71.6 

48 

118.4 

73 

163.4 

98 

208.4 

23 

73.4 

49 

120.2 

74 

165.2 

99 

210  2 

24 

75.2 

50 

122.0 

.  75 

167.0 

100 

212.0 

25 

77.0 

One  deg.  Fahr.=.5556  deg.  centigrade. 
One  deg.  centigrade=1.8  deg.  Fahr. 

To  convert  Fahr.  to  centigrade,  subtract  32,  multiply  by  5  and  divide  by  9. 
To  convert  centigrade  to  Fahr.,  multiply  by  9,  divide  by  5  and  add  32. 
If  temperature  is  below  freezing,  the  above  formula  should  read  "subtract  from  32"  in  place  of 
"subtract  32"  and  "add  32." 

TABLE  C 

EQUIVALENT  CROSS-SECTIONS  OF  DIFFERENT  SIZE  WIRES 
(Brown  and  Sharpe  Gauge) 


Equiv. 
section 

Number  of  wires  of  various  sizes 

2 

4 

8 

16 

32 

64 

128 

0000 

0 

3 

6 

9 

12 

15 

18 

000 

1 

4 

7 

10 

13 

16 

One  each 

CO 

2 

5 

8 

11 

14 

17 

Iand3 

0 

3 

6 

9 

12 

15 

18 

2  and  4 

1 

4 

7 

10 

13 

16 

3  and  5 

2 

5 

8 

11 

14 

17 

4  and  6 

3 

6 

9 

12 

15 

18 

5  and  7 

4 

7 

10 

13 

16 

6  and  8 

5 

8 

11 

14 

17 

7  and  9 

6 

9 

12 

15 

18 

8  and  10 

7 

10 

13 

16 

9  and  11 

8 

11 

14 

17 

] 

10  and  12 

9 

12 

15 

18 

11  and  13 

10 

13 

16 

12  and  14 

11 

14 

17 

13  and  15 

12 

15 

18 

14  and  16 

13 

16 

° 

15  and  17 

14 

17 

16  and  18 

15 

18 



TABLE  D 


401 


COMPARATIVE  TABLE  OF  WIRE  GAUGES 


American  Wire  Gauge 
(Brown  &  Shame) 

Birmingham  Wire  Gauge 

(Stubs) 

Standard  Wire  Gauge 

Gauge 
No. 

Diameter 

Area 

Diameter 

Area 

Diam'ter 

4rea 

Inches 

Circular 
Mills 

Inches 

Circular 
Mills 

Inches 

Circular 
Mills 

7-0 

0.500 

250000. 

6-0 

0.404 

2  15300. 

5-0 

0.432 

1  86600. 

4-0 

0.4600 

211  600. 

0.451 

208  100. 

0.400 

160000. 

3-0 

0.4096 

167  800. 

0.425 

180600. 

0.372 

1  38400. 

2-0 

0  3648 

133100. 

0.380 

144  400. 

0.348 

1  21100. 

1-0 

0.3249 

105  500. 

0.340 

115600 

0.324 

105000. 

1 

0  2893 

83690. 

0.300 

90000. 

0.300 

90000. 

2 

0  257  6 

66  370. 

0.284 

80660. 

0  276 

76180. 

3 

0.2294 

52630. 

0.259 

67080. 

0.252 

63500. 

4 

0.2043 

41  740. 

0.238 

56640. 

0.232 

53820. 

5 

0.1819 

33100 

0.220 

48400. 

0.212 

44940. 

6 

0.1620 

26250. 

0.203 

41  210. 

0.192 

36860. 

7 

0.1443 

20  820. 

0.180 

32400. 

0.176 

30980. 

8 

0.1285 

16  510. 

0.165 

27230. 

0.160 

256oO. 

9 

0.1144 

13090. 

0.148 

21900. 

0.144 

20740. 

10 

0.1019 

10380. 

0.134 

17960. 

0.128 

16380. 

11 

009074 

8234. 

0.120 

14400. 

0.116 

13460. 

12 

0.08081 

6530. 

0.109 

11880. 

0.104 

10820. 

13 

0.071  96 

5178. 

0.0950 

9025. 

0.092 

8464. 

14 

0.06408 

4107. 

0.083  0 

6889. 

0.080 

6400. 

15 

0.05707 

3257. 

0.0720 

5184. 

0.072 

5184. 

16 

0.05082 

2583. 

0.0650 

4225. 

0.064 

4096. 

17 

0.04526 

2048. 

0.0580 

3364. 

0.056 

3136. 

18 

0.04030 

1624. 

0.0490 

2401. 

0.048 

2304. 

19 

0.03589 

1288. 

0.0420 

1764. 

0.040 

1600. 

20 

0.03196 

1022. 

0.0350 

1225. 

0.036 

1296. 

21 

0.02846 

810.1 

0.0320 

1024. 

0.032 

1024. 

22 

0.025  35 

642.4 

0.0280 

784. 

0.028 

784.0 

23 

0.02257 

509.5 

0.0250 

625. 

0.024 

576.0 

24 

0.020  10 

404.0 

0.0220 

484. 

0.022 

484.0 

25 

0.01790 

320.4 

0.0200 

400. 

0.020 

400.0 

26 

0.01594 

254.1 

0.0180 

324. 

0.018 

324.0 

27 

0.01420 

201.5 

0.0160 

256. 

0.016  4 

269.0 

28 

0.01264 

159.8 

0.014.0 

196. 

0.014  8 

219.0 

29 

0.01126 

126.7 

0.0130 

169. 

0.013  6 

185.0 

30 

0.01o03 

100.5 

0.0120 

144. 

0.012  4 

153.8 

31 

0.008928 

79.70 

0.0100 

100. 

0.0116 

134.6 

32 

0.007950 

63.21 

0.0090 

81. 

0.0108 

116.6 

33 

0.007080 

50.13 

0.0080 

64. 

0.0100 

100.0 

34 

0.006305 

39.75 

0.0070 

49. 

0.0092 

84.64 

35 

0.005615 

31.52 

0.0050 

25. 

0.0084 

70.56 

36 

0.005000 

25.00 

0.0044 

16. 

0.0076 

67.76 

37 

0  004  453 

19.83 

0  0068 

46.24 

38 

0.003965 

15.72 

0.0060 

36.00 

39 

0  003  531 

12.47 

0  0052 

27  04 

40 

0.003145 

9.888 

0.0048 

23.04 

41 

0.0044 

19.36 

402 


TABLE  E 


COPPER  WIRE  TABLE  OF  AMERICAN 
Giving  Weights  and  Lengths  of  cool,  warm  and  hot  wires, 


B.&S. 
or 
A.  W.  G. 

Diameter 

Area 

Lbs.  Per 
Foot 

Inches 

Circular 
miles 

Sq.  in. 
Sq.  miles 

68°  F. 
20°  C. 

0000 

0.460 

211600 

166  190 

0.6405 

13090 

000 

0.4096 

167800 

131  790 

0.5080 

8232 

00 

0.3648 

133100 

104518 

0.4028 

5177 

0 

0.3249 

105500 

82887 

0.3195 

3256 

1 

0.289  3 

83  690 

65732 

0.2533 

2048 

2 

0.257  6 

66370 

52128 

0.2009 

1288. 

3 

0.2294 

52630 

41339 

0.  159  3 

810.0 

4 

0.2043 

41  740 

32784 

0.1264 

509.4 

5 

0.1819 

33100 

25999 

0.1002 

320.4 

6 

0.1620 

26250 

20  618 

0.079  46 

2015 

7 

0.1443 

20820 

16351 

0.6302 

126.7 

8 

0.1285 

16  510 

12967 

0.04998 

79.69 

9 

0.1144 

13090 

10283 

0.03963 

50.12 

10 

0.1019 

10380 

8155 

0.03143 

31.52 

11 

0.09074 

8234 

6467 

0.024  93 

19.82 

12 

0.08081 

6530 

5129 

0.01977 

12.47 

13 

0.071  96 

5178 

4067 

0.01.568 

7.840 

14 

0.06408 

4107 

3225 

0.01243 

4.931 

15 

0.05707 

3257 

2558 

0.009  858 

3.101 

16 

0.05082 

2583 

2029 

0.007818 

1.950 

17 

0.04526 

2048 

1609 

0.006200 

1.226 

18 

0.04030 

1624 

1276 

0.004917 

0.771  3 

19 

0.03589 

1288 

1012 

0.003899 

0.4851 

20 

0.031  96 

1022 

802 

0.003092 

0.3051 

21 

0.02846 

810.1 

632.3 

0.002452 

0.1919 

22 

0.025  35 

642.4 

504.6 

0.001  945 

0  1207 

23 

0.02257 

509.5 

400.2 

0.001  542 

0.07589 

24 

0.020  10 

404.0 

317.3 

0.001  223 

0.04773 

25 

0.01790 

324.4 

251.7 

0.000  969  9 

0.03002 

26 

0.015  94 

254.1 

199.6 

0.0007692 

0.01888 

27 

0.0142 

201.5 

158.3 

0.0006100 

0.011  87 

28 

0.01264 

159.8 

125.5 

0.0004837 

0.007466 

29 

0.01126 

126.7 

99.53 

0.0003836 

0.004  696 

30 

0.01003 

100.5 

78.94 

0.0003042 

0.002953 

31 

0.008928 

79.70 

62.60 

0.0002413 

0.001857 

32 

0.007  950 

63.21 

49.64 

0.0001913 

0.001  168 

33 

0.007080 

50.13 

39.37 

0.000  1517 

0000  734  6 

34 

0.006  305 

39.75 

31.22 

0.0001203 

0.0004620 

35 

0.005  615 

31.52 

24.76 

0.00009543 

0.0002905 

36 

0.0050 

25.0 

19.64 

0.00007568 

0.0001827 

37 

0.004  453 

19.83 

15.57 

0.00006001 

0.0001149 

38 

0.003965 

15.72 

12.35 

0.00004759 

0.00007210 

39 

0.003  531 

12.47 

9.79 

0.00003774 

0.00004545 

40 

0.003  145 

9.888 

7.77 

0.00002993 

0.00002858 

TABLE  E 


403 


INSTITUTE  OF  ELECTRICAL  ENGINEERS 
of  Matthiessen's  standard  of  conductivity. 


Ibs.  per 
Ohm. 

Feet  Tier 
Pound 

Feet  Per 
ohm 

122°  F. 
50°  C. 

176°  F. 

80°  C. 

68°  F. 
20°  C. 

122°  F. 
50°  C. 

176°  F. 
80°  C. 

11720 

10570 

1.561 

20440 

18290 

16510 

7369 

6647 

1.969 

16210 

14510 

13090 

4634 

4  182 

2.482 

12850 

11500 

10380 

2914 

2630 

3  130 

10190 

9  123 

8232 

1833 

1654 

3.947 

8083 

7235 

6528 

1153 

1040 

4.977 

6410 

5738 

5177 

725.0 

654.2 

6.276 

5084 

4550 

4106 

455.9 

411.4 

7.914 

4031 

3608 

3256 

286.7 

258.7 

9.980 

3  1<V7 

2862 

2582 

180.3 

162.7 

12.58 

2535 

2269 

2048 

113.4 

102.3 

15.87 

2011 

1800 

1624 

71.33 

64.36 

20.01 

1595 

1427 

1288 

44.86 

40.48 

25.23 

1265 

1  132 

1021 

28.21 

25.46 

31.82 

1003 

897.6 

809.9 

17.74 

16.01 

40.12 

795.3 

711.8 

642.3 

11.16 

10.07 

50.59 

603.7 

564.5 

509.4 

7.017 

6.332 

63.79 

500.1 

447.7 

404.0 

4.413 

3.982 

80.44 

396.6 

355.0 

320.3 

2.776 

2.504 

101.4 

314.5 

281.5 

254.0 

1.746 

1.575 

127.9 

249.4 

223.3 

201.5 

1.098 

0.990  6 

161.3 

197.8 

177.1 

159.8 

0.6904 

0.6230 

203.4 

156.9 

140.4 

126.7 

0.434  2 

0.3918 

256.5 

124.4 

111.4 

100.5 

0.273  1 

0.2464 

323.4 

98.66 

88.31 

98.68 

0.1717 

0.1550 

407.8 

78.24 

70.03 

63.19 

0.1080 

0.09746 

514.2 

62.05 

55..  54 

50.11 

0.06793 

0.061  29 

648.4 

49.21 

44.04 

39.74 

0.042  72 

0.038  55 

817.6 

39.02 

34.93 

31.52 

0.02887 

0.02424 

1  031 

30.95 

27.70 

24.99 

0.01690 

0.015  25 

1300 

24.54 

21.97 

19.82 

0.01063 

0.009  588 

1639 

19.46 

17.42 

15.72 

0.006683 

0.006030 

0067 

15.43 

13.82 

12.47 

0.004203 

0.003792 

2607 

12.24 

10.96 

9.886 

0.002643 

0.002  385 

3287 

9.707 

8.688 

7.840 

0.001  662 

0.001  500 

4  145 

7.698 

6.890 

6.217 

0.001  045 

0.000  943  6 

5227 

6.105 

5.464 

4.930 

0.0006575 

0  000  593  3 

6591 

4.841 

4.333 

3.910 

0.0004135 

0.000373  1 

8311 

3.839 

3.436 

3.101 

0.0002601 

0.0002347 

10480 

3  045 

2.725 

2.459 

0.0001636 

0.0001476 

13210 

2.414 

2.161 

1.950 

0.0001029 

0.00009281 

16660 

1.915 

1.714 

1.547 

0.00006454 

0.00005824 

21010 

1.519 

1.359 

1.226 

0.00004068 

0.00003671 

26500 

1.204 

1.078 

0.9726 

0.00002559 

0  000  023  09 

33  410 

0  9550 

0.8548 

0.771  3 

404 


TABLE  F 


COPPER  WIRE  TABLE  OF  AMERICAN 
Giving  Resistances  of  cool,  warm  and  hot  wires, 


B.  &  S. 
or 
A.  W.  G. 

Ohms  per  Pound. 

68°  F. 
20°  C. 

122°  F.                                176°  F. 
50°  C.                   ;              80°  C. 

0000 

0.00007639 

0.00008535 

0.00009459 

000 

0.0001215 

0.0001357 

0.0001504 

00 

0.000  193  1 

0.0002158 

0.000239  1 

0 

0.0003071 

0.0003431 

0.0003803 

1 

0.0004883 

0.0005456 

0.0006040 

2 

0.0007765 

0.000  867  5 

0.0009614 

3 

0.001  235 

0.001  379 

0.001529 

4 

0.001  963 

0.002  193 

0.002431 

5 

0.003  122 

0.003487 

0.003865 

6 

0.004  963 

0.005  545 

0.006  145 

7 

0.007892 

0.008  817 

0.009772 

8 

0.012  55 

0.014  02 

0.01554 

9 

0.019  95 

0.022  29 

0.024  71 

10 

0.031  73 

0.0345 

0.03928 

11 

0.05045 

0.056  36 

0.06246 

12 

0.08022 

0.08962 

0.09932 

13 

0.1276 

0.1425 

0.1579 

14 

0.2028 

0.226  6 

0.251  1 

15 

0.3225 

0.3603 

0.3993 

16 

0.5128 

0.5729 

0.6349 

17 

0.815  3 

0.9109 

1.010 

18 

1.296 

1.448 

1.605 

19 

2.061 

2.303 

2.552 

20 

3.278 

3.662 

4.058 

21 

5.212 

5.823 

6.453 

22 

8.287 

9.259 

10.26 

23 

13.18 

14.72 

16.32 

24 

20.95 

23.41 

25.94 

25 

33.32 

37.22 

41.25 

26 

52.97 

59.18 

65.59 

27 

84.23 

94.11 

104.3 

28 

133.9 

149.6 

165.8 

29 

213.0 

237.9 

263.7 

30 

338.6 

378.3 

419.3 

31 

538.4 

601.6 

666.7 

32 

856.2 

956.5 

1060 

33 

1361 

1521 

1685 

34 

2165 

2418 

2680 

35 

3441 

3845 

4262 

36 

5473 

6114 

6776 

37 

8702 

9722 

10770 

38 

13870 

15490 

17170 

39 

22000 

24580 

27240 

40 

34980 

39080 

43320 

TABLE  F 


405 


INSTITUTE  OF  ELECTRICAL  ENGINEERS 
of  Matthiessen's  standard  of    conductivity. 


Ohms  per  foot. 

B.  &S. 
or 
A.  W.  G. 

68°  F. 
20°  C. 

122°  F. 
50°  C. 

176°  F. 
80°  C. 

0.00004893 

0.000  054  67 

0.00006058 

0000 

0.00006170 

0.00006893 

0.00007640 

000 

0.00007780 

0.00008692 

0.00009633 

00 

0.00009811 

0,000  1096 

0.0001215 

0 

0.0001237 

0.0001382 

0.0001532 

1 

0.0001560 

0.0001743 

0.0001932 

2 

0.0001967 

0.0002198 

0.0002435 

3 

0.0002480 

0.0002771 

0.0003071 

4 

0.0003123 

0.0003495 

0.0003873 

5 

0.0003944 

0.0004406 

0.0004883 

6 

0.0004973 

0.0005556 

0.0006158 

7 

0.0006271 

0.0007007 

0.0007765 

8 

0.0007908 

0.0008835 

0.0009791 

9 

0.0009972 

0.001  114 

0.001  235 

10 

0.001257 

O.OOJ  405 

0.001  557 

11 

0  001  586 

0  001771 

0.001963 

12 

0.001999 

0.002234 

0.002  476 

13 

0.002521 

0.002817 

0.003  122 

14 

0  003  179 

0.003552 

0.003936 

15 

0.004009 

0.004479 

0.004964 

16 

0.005055 

0.005  648 

0.006  259 

17 

0.006374 

0.007  122 

0.007  892 

18 

0.008038 

0.008980 

0.009952 

19 

0.01014 

0.011  32 

0.012  55 

20 

0.01278 

0.01428 

0.01583 

21 

0.016  12 

0.01801 

0.01096 

22 

0.02032 

0.02271 

0.025  16 

23 

0.02563 

0.02863 

0.031  73 

24 

0.032  31 

0.036  10 

0.041  10 

25 

0.04075 

0.04552 

0.05045 

26 

0.051  38 

0.05740 

0.06362 

27 

0.06479 

0.07239 

0.08022 

28 

0.081  70 

0.09128 

0.1012 

29 

0.1030 

0.115  1 

0.1276 

30 

0.1299. 

0.1451 

0.1608 

31 

0.1638 

0.1830 

0.2028 

32 

0.2066 

0.2308 

0.2558 

33 

0.2605 

0.2910 

0.3225 

34 

0.3284 

0.3669 

0.4067 

35 

0.4142 

0.4627 

0.5129 

36 

0.5222 

0.5835 

0.6466 

37 

0.6585 

0.7357 

0.8154 

38 

0.8304 

0.927  7 

1.028 

39 

1.047 

1.170 

1.296 

40 

406 


TABLE  G 


TABLE  OF  CARRYING  CAPACITY  OF  WIRE  AS  ESTABLISHED  BY  THE 
NATIONAL  BOARD  OF  UNDERWRITERS 


Copper 
B.  &  S.  G. 

Circular 
Mils. 

Rubber  Cover- 
ed Wires, 
Amperes 

Other 
Insulations 
Amperes 

18 

1  624 

3 

5 

16 

2583 

6 

8 

14 

4  107 

12 

16  - 

12 

6530 

17 

23 

10 

10380 

24 

32 

8 

16  510 

33 

46 

6 

26250 

46 

65 

5 

33  100 

54 

77 

4 

41  740 

65 

92 

3 

52630 

76 

110 

2 

66370 

90 

131 

1 

83690 

107 

156 

0 

105  500 

127 

185 

00 

133  100 

150 

220 

000 

167  800 

177 

265 

0000 

211  600 

210 

312 

200  000 

200 

300 

300  000 

270 

400 

400  000 

330 

500 

500  000 

390 

590 

600  000 

450 

680 

700  000 

500 

760 

800  000 

550 

840 

900  000 

600 

920 

1  000  000 

650 

1  000 

1  100  000 

690 

1080 

1  200  000 

730 

1  150 

1  300  000 

770 

1220 

1  400  000 

810 

1290 

1  500  000 

850 

1360 

1  600  000 

890 

1  430 

1  700  000 

930 

1  490 

1  800  000 

970 

1  550 

1  900  000 

1010 

1  610 

2  000  000 

1050 

1670 

The  question  of  drop  is  not  taken  into  consideration  in  the 
above  table. 


TABLE  H 


407 


DIAMETER  OF  WIRE  WHICH  WILL  FUSE  WITH  GIVEN  CURRENT 
(W.  H.  Preece.) 


Diameter  in  Mils 

Amp. 

Copper 

Alum- 

Plat- 

German 

Plat- 

Iron 

Tin 

Tin  lead 

Lead 

inium 

inium 

silver 

inoid 

alloy 

1 

2 

2.1 
3.4 

2.6 
4.1 

3.3 
5.3 

3.3 
5.3 

3.5 

5.6 

4.7 

7.4 

7.2 
11.3 

8.3 
13.2 

8.1 
12.8 

3 

4.4 

5.4 

7.0 

6.9 

7.4 

9.7 

14.9 

17.3 

16.8 

4 

5.3 

6.5 

8.4 

8.4 

8.9 

11.7 

18.1 

21.0 

20.3 

5 

6.2 

7.6 

9.8 

9.7 

10.4 

13.6 

21.0 

24.3 

23.6 

10 

9.8 

12.0 

15.5 

15.4 

16.4 

21.6 

33.4 

38.6 

37.5 

15 

12.9 

15.8 

20.3 

20.2 

21.5 

28.3 

43.7 

50.6 

49.1 

20 

15.6 

19.1 

24.6 

24.5 

26.1 

34.3 

52.9 

61.3 

59.5 

25 

18.1 

22.2 

28.6 

28.4 

30.3 

39.8 

61.4 

71.1 

69.0 

30 

20.5 

25.0 

32.3 

32.0 

34.2 

45.0 

69.4 

80.3 

77.9 

35 

22.7 

27.7 

35.8 

35.6 

37.9 

49.8 

76.9 

89.0 

86.4 

40 

24.8 

30.3 

39.1 

38.8 

41.4 

54.5 

84.0 

97.3 

94.4 

45 

26.8 

32.8 

42.3 

42.0 

44.8 

58.9 

90.9 

105.2 

102.1 

50 

28.8 

35.2 

45.4 

45.0 

48.0 

63.2 

97.5 

112.9 

109.5 

60 

32.5 

39.7 

51.3 

50.9 

54.2 

71.4 

110.1 

127.5 

123.7 

70 

36.0 

44.0 

56.8 

56.4 

60.1 

79.1 

122.0 

141.3 

137.1 

80 

39.4 

48.1 

62.1 

61.6 

65.7 

86.4 

133.4 

154.4 

149.9 

90 

42.6 

52.0 

67.2 

66.7 

71.1 

93.5 

144.3 

167.1 

162.1 

100 

45.7 

55.8 

72.0 

71.5 

76.2 

100.3 

154.8 

179.2 

173.9 

120 

51.6 

63.0 

81.4 

80.8 

86.1 

113.3 

174.8 

202.4 

196.4 

140 

57.2 

69.8 

90.2 

89.5 

95.4 

125.5 

193.7 

224.3 

217.6 

160 

62.5 

76.3 

98.6 

97.8 

104.3 

137.2 

211.8 

245.2 

237.9 

180 

67.6 

82.6 

105.6 

105.8 

112.8 

148.4 

229.1 

265.2 

257.3 

200 

72.5 

88.6 

114.4 

113.5 

121.0 

159.2 

245.7 

284.5 

276.0 

225 

78.4 

95.8 

123.7 

122.8 

130.9 

172.2 

265.8 

307.7 

298.6 

250 

84.1 

102.8 

132.7 

131.7 

140.4 

184.8 

285.1 

330.1 

320.3 

275 

89.7 

109.5 

141.4 

140.4 

149.7 

196.9 

303.8 

351.8 

341.3 

300 

95.0 

116.1 

149.8 

148.7 

158.6 

208.6 

322.0 

372.8 

361.7 

408 


* TABLE  I 

RING  ARMATURE  WINDINGS 


J° 


TH  <N 


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jb 

CO 
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ft 
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ft 
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* TABLE  J 

WAVE-WOUND  DRUM  ARMATURE  WINDINGS 


409 


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Smpui^    1               j_| 

<N 

CO 

^ 

410 


p 


* TABLE  K 

LAP-WOUND  DRUM  ARMATURE  WINDINGS 

F-H  <N  CO 


*JM 


1 


JSi 


tS3 


fc 

I1 

P5 


—  Q 

-£ 


X! 


-H 


-fl 


-H 


?: 

-H 


UI    = 

da^g  pptj 


O 


X! 
ft 


-f: 


N 


li 


. 

CN 


TABLE  M 


411 


WIRING  TABLE  FOR  TWO  PER  CENT  LOSS  ON  A  50-VOLT  CIRCUIT 
Table  for  1  Volt  Loss 


i 

M  -H  cs  oo  co  »o  us  T*  cocoiMCN^HOOQQOgg 

0 

i 

CO    (M    O    O5    1--    tO    fO    «5-<l<Tt<C<3CO<>Ji-H^HOOOOoO 
0° 

§ 

-*C^~HC500t^cO»O   "3  ^"  •*  W  C^l  (M  1-1  I-H  O  O  g  ^  Q  O 
00 

S5 

0 
H 

§ 

Tt<CO-HOOOI>.l>-!»    lOtOTjlTjtcOC^iM'-HOO  QOOO  O 

00 

« 

53 

&<?> 

§ 

»O  IcC    OJ    O    OJ    OO    t>-    t—    O»OiOTt«^<COC^<M-HOOgOgOOO 

5    ^8SS 

1                                                                                                  oo 

B| 

g^ 

§ 

«o|^j  co  I-H  o  01  oo  r-  o-totouo^^ccccc^^H  ooooooo  QQ  o 
ooo 

§1 
I" 

8 

CO   «O    CO   (M    O   O3    OS   OO    t^t^OcOiC'«*i^irOiMiM-HOOOOOOOOO 

1-H     ^H      rt     1-H     i-H                                                                                                                                             OOOggOSl 

0 

S'l 

^  '! 

8 

I    »O    •<*(    (M    T-H    O    O5    OO    00  t^  !>•  <O  "3  "5  -1*1  Tt<  COIM  i-c  i-H  O  O  g  g  OggOg  g 

:                                                                                      oo 

gs 

§ 

•   I-H  jj^H   I-I,-H^HT-(                                                                                                       OOOoSj 

8 

•    lOfCO    <M    -H    O    O    OJOOOO  !>-^-!O"5»OTficOC^  (Mr-ti-H  OO  O  OO  OOO 

•     1-1  I-H     »-H     i-H     r-t     i—  1 

g 

S 

•    CO  ••*    CO    (M    ^H    O    OO5O5OO^-l>'«OCOiO^COCO(MC^'^'-^r-iOOOg55 

1 

s 

•    <O    "5|£2    (N    IM    »^    O  O  OS  OS  00  t»  O-  CO  1C  >O  Tfi  CO  CO  C<l  (M  <M  -H  r-^  TH  O  O  O 

i 

9 

Q 

5 

:    :    :  ^T  -•  "•  -  -"-*-"-1 

3 

.    .    .  SSpS2  S  2^32°" 

8 

•    IO    tQygj    CO    CO  (M  <M  -H  O  O  O>  O5  00  t^  CO  CO  >O  1C  Tf  Tfl  Tfi  CO  CO  CO  W  N 

S 

:    :    :    :  s  s  SF  2222^2^ 

8 

o| 

4 

^^CNCO^^cOt^   OOO.OCN^COOOO^OJO^.nOJggJgOJOggg 

412 


TABLE  N 


WIRING  TABLE  FOR  TWO  PER  CENT  LOSS  OX  A  110- VOLT  CIRCUIT 
Table  for  2.2  Volts  Loss 


DISTANCE  IN  FEET  TO  CENTER  OF  DISTRIBUTION 
(Wire  sizes  in  B.  &  S.  Gauge) 

§ 

rs=^ 

00 

§ 

00 

i 

S|SSS»» 

o  o 

i 

i!i: 

00 

1 

T 

"H°83g5§Sg 

00 

1 

T 

oo 

1 

1                                                                                                             oo 

S 

sts= 

0 

i 

SIS  S  S 

1 

2|S  2  S  S  3S  °>°>  ««—  r—  *.«*.««oe,  —  oggg 

8 

•  sis  2 

CM    *—  '  »—  *    OO    O>  OO  OO    t*~  t^«  to  1C  ^  ^  CO  CO  CM  '-H  I-H  O  O  O 

g  •     ...  ^i^,  ^ 

2  22  S3  2—  oooo^tooo^^coc.^^^0 

tO                   •          •          •          •     2     -H 

g^g-gS-^o-5-oor.^.o-s^^eo-. 

0              .....   to 

2133  22  £232  SS0*001^500"5"* 

^                •    •    :    :  2  i22I^S  222  2  3  S  ^  ""  ^  l'  l'"  u" 

g       :::::: 

:  22  S2ISS2  SSSSS030- 

en 

21 

10 

TABLE  0 


413 


WIRING  TABLE  FOR  TWO  PER  CENT  LOSS  ON  A  220-VOLT  CIRCUIT 
Table  for  4.4  Volts  Loss 


DISTANCE  IN  FEET  TO  CENTER  OF  DISTRIBUTION 
(Wire  sizes  in  B.  &  S.  Gauge) 

No.  of 
amperes 

Si 

3 

-=- 

3 

3 

S 

8 

B 

8 

§ 

fj 

1 

§ 

1 

1 

1 

1 

1 

1 

1 

16 

1.5 

16 

15 

M 

2 

16 

15 

15 

""  TT-TT 

3 

16 

15 

15 

"IT 

"IT 

T3 

12           15! 

4 

16 

15 

15 

13 

13 

13 

12 

12 

11 

11 

5 

16 

15 

T4 

13 

13 

13 

12 

11 

11 

10         10 

6 

16 

15 

15 

13 

14 

13 

12 

12 

11 

11 

10 

9 

9 

7 

16 

15 

T4 

T4 

14 

13 

12 

12 

11 

11 

10 

9 

9 

8 

8 

16 

15 

15 

14 

14 

13 

12 

12 

11 

11 

10 

9 

9 

8 

8 

9 

15 

15 

13 

14 

13 

12 

12 

11 

11 

10 

9 

9 

8 

8 

7 

10 

16 

15 

14 

14 

13 

13 

12 

11 

11 

10 

10 

9 

8 

8 

7 

7 

12 

16 

15 

14 

14 

13 

12 

12 

11 

11 

10 

9 

9 

8 

8 

7 

7 

6 

14 

16 

15 

14 

14 

13 

12 

12 

11 

11 

10 

9 

9 

8 

7 

7 

6 

6 

5 

16 

16 

15 

14 

13 

12 

12 

11 

11 

10 

9 

9 

8 

8 

7 

7 

6 

6 

5 

18 

15 

14 

13 

12 

11 

11 

10 

9 

9 

8 

8 

7 

7 

6 

5 

5 

4 

20 

16 

15 

14 

13 

12 

11 

11 

10 

10 

9 

8 

8 

7 

7 

6 

5 

5 

4 

4 

25 

16 

14 

13 

12 

[1 

10 

10 

9 

9 

8 

7 

7 

6 

6 

5 

4 

4 

3 

3 

30 

15 

13 

[2 

11 

10 

10 

9 

9 

8 

7 

7 

6 

6 

5 

4 

4 

3 

3 

2 

35 

1 

13 

[j 

10 

10 

9 

8 

8 

7 

7 

6 

5 

5 

4 

4 

3 

2 

2 

1 

40 

14 

12 

[j 

10 

9 

8 

8 

7 

7 

6 

5 

5 

4 

4 

3 

2 

2 

1 

1 

45 

13 

12 

10 

9 

9 

8 

7 

7 

6 

6 

5 

4 

4 

3 

3 

2 

1 

1 

0 

50 

13 

10 

9 

8 

7 

7 

6 

6 

5 

4 

4 

3 

3 

2 

1 

1 

0 

0 

60 

12 

[0 

9 

8 

7 

6 

6 

5 

4 

4 

3 

3 

2 

1 

1 

0 

0 

00 

70 

11 

10 

8 

7 

• 

6 

5 

5 

4 

4 

3 

2 

2 

1 

1 

0 

00 

00 

000 

80 

11 

9 

8 

7 

6 

5 

5 

4 

4 

3 

2 

2 

1 

1 

0 

00 

00 

000 

000 

90 

10 

9 

7 

6 

6 

5 

4 

4 

3 

3 

2 

1 

1 

0 

00 

00 

000 

000 

0000 

100 

10 

8 

j 

6 

5 

4 

4 

3 

3 

2 

1 

1 

0 

0 

00 

000 

000 

0000 

0000 

120 

9 

7 

6 

5 

4 

4 

31  3 

2 

1 

1 

0 

0 

00 

000 

000 

0000 

0000 

414 


SYMBOLS  FOR  WIRING  PLANS 


STANDARD    SYMBOLS    FOR    WIRING    PLANS 
IU1101UI  OKTUCAl  COXTtACTORS  ASSOCIATION  OF  THE  IWITED  STATEs"»a*  THE  AMERICAN  INSTITUTE  OF  ARCHITECTS, 


{4}  Ceilint  Outlet;  Electric  only.    Humeral  in  center  indicates  numoer  of  Standard  16  C.  P.  Incandescent  Lasps. 

3J£  Ceiling  Outlet;  Combination.  }  indicate!  4-16  C.  P.  Standard  Incandeicent  Lampi  and  2  Oai  Buraen.  If  gai  i 

§-@  Bracket  Outlet;  Electric  only.  Humeral  in  center  indicate!  number  of  Sta  ndard  16  C.  P.  Incandeicent  Lam; 

?HXJ  f  Bracket  Outlet;  Combination,  j  indicate!  4-16  C.  P.  Standard  Incandeicent  Lamp,  and  2  Oai  Burnen.  If  ga: 

^-{5  Wall  or  Baseboard  Beceptacle  Outlet.  Humeral  in  center  indicates  number  of  Standard  16  C.  P.  Incandeicen 

^  Floor  Outlet.    Humeral  in  center  indicates  number  of  Standard  16  C.  P  Incandeicent  Lamps. 

JJ 6  Outlet  for  Outdoor  Standard  or  Pedestal;  Electric  only.    Humeral  indicates  number  of  Stand  16  C  P.  Lamps 

0|  Outlet  for  Outdoor  Standard  or  Pedestal;  Combination,    f  indicates  6-16  C.  P.  Stand.  Incan.  Lamp:  6  Oai  B 

J§{  Drop  Cord  Outlet 

®  One  Light  Outlet,  for  Lamp  Eeccptaele. 

3  Arc  Lamp  Outlet 

Q  Special  Outlet,  for  Lighting,  Heating  and  Power  Current,  as  described  in  Specification!. 

CQo  CeUil*  Fan  °"Uet- 

Show  ai  many  Symbols  as  there  are  Switches.  Or  in  case  of  a  very  large  group 
of  Switches,  indicate  number  of  Switchei  by  a  Roman  numeral,  thai:  S>  XII. 
meaning  12  Single  Pole  Switchei. 

Describe  Type  of  Switch  in  Specification!,  that  is, 

Flush  or  Surface,  Push  Button  or  Snap, 


8.  P.  Switch  Outlet. 
D.  P.  Switch  Outlet. 
8-Wey  Switch  Outlet. 
4- Way  Switch  Outlet 
automatic  Door  Switch  Outlet 
Electrolier  Switch  Outlet 


a 


Diitribution  Panel 

Junction  or  Pull  Box. 

Motor  Outlet;  Numeral  in  center  Indicate!  Rone  Power. 

Motor  Control  Outlet 


•  Main  or  Feeder  ran  concealed  under  Floor. 

Feeder  ran  concealed  under  Floor  above. 


•  Branch  Circuit  run  concealed  under  Floor. 

•  Branch  Circuit  ran  concealed  under  Floor  then. 


-© 

4 

HD 

fJJ 


Telephone  Outlet;  Public  Sen-ice. 

Bell  Outlet 

Butter  Outlet. 

Push  Button  Outlet ;  Humeral  indicates  number  of  Pushes, 

Annunciator;  Humeral  indicates  aaaate  rf  Pointa. 

Speaking  Tube. 

Watchman  Clock  Outlet. 

Watchman  Station  Outlet. 

Matter  Time  Clock  Outlet. 

Secondary  Time  Clock  Outlet 

Door  Opener. 

Special  Outlet ;  Tor  Signal  Systems,  as  described  In  Specttettlont. 


SUCCESTIONS  IN 

DARD  SYMBOLS  FOR 


PLANS 


It  la  Important  that  ample-  apace  be 
allowed  for  the  initallatlon  of  main*,  feed- 
en,  branches  and  distribution  panels. 

It  li  desirable  that  a  key  to  the  symbols 
used  accompany  all  plans 

If  mains,  feeders,  branches  and  die- 
tribution  panels  are  shown  on  the  plena, 
it  la  desirable  that  they  be  designated  by 
letters  or  numbers. 

Hdf  hts  of  Centre  ol  Wall  Outlets  (uolcai 
otherwise  specified) 

LlTinj  Rooms  5'    8" 

Chambers  •'    0" 

Offices  «'    0' 

Corridor!  6'    3' 

Height  of  Switchei  (unless  otherwise  spcc- 

Uied)  '  4'    0- 


Copyrighted 


I  Circuit  for  Clock,  Telephone,  Bell  or  other  Serrice,  ran  under  Floor,  concealed 
(Kind  of  Service  wanted  ascertained  by  Symbol  to  which  line  connects. 
( Omit  for  Clock,  Telephone,  Bell  or  ether  Serrlce.  ran  under  Poor  abore,  concealed. 
\  Kind  of  Serrioe  wanted  ascertained  by  Symbol  to  which  line  connect!. 

ROTX— If  ether  than  Standard  18  C.  P.  Incandescent  lamps  an 
Bpecdnoatloni  should  describe  capacity  of  Lamp  to  be  uted. 


PRACTICAL  APPLIED  ELECTRICITY 


415 


SUMMARY    OF 


DIRECT-    AND    ALTERNATING-CURRENT 
RELATIONS 


SYNOPSIS   OF   UNITS   AND   SYMBOLS   IN   GENERAL   USE 


Unit 

Name 

Symbols 

DEFINING  EQUATIONS 

Direct 
Current 

Alternating 
Current 

Electromotive 
Force 
Current 
Resistance 
Power 
Impedance 
Reactance 
Inductance 
Capacity 
Quantity 
Admittance 
Conductance 
Susceptance 

Volt 
Ampere 
Ohm 
Watt 
Ohm 
Ohm 
Henry 
Farad 
Coulomb 
Mho 
Mho 
Mho 

E,  e 
I,    i 
R.   r 
P 

Z,   z 
X,  x 

L,    1 
C,    c 
Q,   Q 
Y,   y 
G,  g 
B,  b 

IR 
E-^-R 

El 

QX-M«: 

IXtime 
I-^R 

IZ 
E+Z 

VZ2  —  X2 
ElXp.f. 

VR2-f-X2 

VZ2—  R2 

Q-^E 
IXtime 

R-=-Z2=VY2  —  B2 

X+Z^VY'-G2 

*  Linkage=turnsXmagnetic  flux. 


DIRECT-CURRENT  RELATIONS 

Electromotive  Force,  represented  by  E  or  e. 

Current  times  resistance  I  X  R. 

Watts  divided  by  current  P  -f- 1. 
Current,  represented  by  I  or  i. 

E.m.f.  divided  by  resistance  E  -=-  R. 

Watts  divided  by  e.m.f.  P-=-E.. 
Resistance,  represented  by  R  or  r. 

E.m.f.  divided  by  current  E  -=-  I. 

Watts  divided  by  square  of  current  P  -f- 12. 
Watts,  represented  by  P. 

E.m.f.  times  current  E  X  I. 

Square  of  current  times  resistance  I2  X  R. 

Square  of  e.m.f.  divided  by  resistance  ES  •—  R. 
Resistances  in  Series. 

The  total  resistance  of  a  number  of  resistances  in  series  is 
equal  to  the  sum  of  all  of  them.  R  =  Rx  +  R.,  +  R3  +.  .  . 


416  PRACTICAL  APPLIED  ELECTRICITY 

Resistances  in  Parallel. 
The  joint  resistance  of  two  resistances  in  parallel  is  equal 

to  their  product  divided  by  their  sum.    R  =  (Ri  X  R?)  — 

(Ri  +  Ro). 
The  joint  resistance  of  a  number  of  resistances  connected 

in  parallel  is  the  reciprocal  of  the  sum  of  the  reciprocals. 


R!       R2       R3       '  '  '  ' 

If  conductance  is  used  in  place  of  resistance,  the  joint 
resistance  is  the  reciprocal  of  the  sum  of  the  conduct- 
ances. 


G,  +  G,  + 


ALTERNATING-CURRENT   RELATIONS 

Impressed  e.m.f.,  represented  by  E. 

Current  times  impedance  I  X  Z. 

Current  divided  by  admittance  I  -r-  Y. 

Inductive  e.m.f.  divided  by  sine  of  lag  or  lead  angle  (re- 
active factor)  E!  -r-  r.f. 

Effective  e.m.f.  divided  by  cosine  of  lag  or  lead  angle 
(power  factor)  Er  -*-  p.f. 

The  square  root  of  the  sum  of  the  squares  of  the  resultant 
reactive  e.m.f.  and  the  effective  e.m.f. 


E  =  VEr2  -f-   (Ei  EC) 2. 

Inductive  e.m.f.,  represented  by  Ej. 

6.28  times  frequency  times  inductance  reactance    =  27rfLI. 
Current  times  inductance  reactance. 
Impressed  e.m.f.  times  sine  of  lag  angle   (reactive  factor) 

if  there  is  no  capacity  E  X  r.f. 

The   square   root   of   the   square   of  impressed,   minus   the 
square  of  effective  e.m.f.  if  the  current  lags  and  there  is 
no  capacity.  ______ 

Ei  =  VE2  — Er2. 

Condensive  e.m.f.,  represented  by  Ec. 
Current    times   one    divided   by   6.28   times   the   frequency 

times  the  capacity  I  X  (1  H-  2irfC). 
Current  times  capacity  reactance  I  X  X... 
Impressed  e.m.f.  times  sine  of  lead  angle  (reactive  factor) 

if  there  is  no  inductance  E  X  r.f. 
The  square  root  of  the  square  of  the  impressed  minus  the 

square   of  the   effective   e.m.f.  if  the   current   leads   and 

there  is  no  inductance. 


PRACTICAL  APPLIED  ELECTRICITY  417 

Effective  e.m.f.,  represented  by  Er. 

Current  times  resistance  I  X  R. 

Current  divided  by  conductance  I  -=-  G. 

True  watts  divided  by  current  P  -j-  I. 

Impressed  e.m.f.  times  cosine  of  lag  or  lead  angle  (power 
factor)    E  X  p.f. 

The    square   root    of   the.  square   of   the   impressed   e.m.f. 

minus  the  square  of  the  reactive  e.m.f. 
Current,  represented  by  I  or  i. 

Effective  e.m.f.  divided  by  resistance  E  -*-  R. 

Effective  e.m.f.  multiplied  by  conductance  E  X  G. 

Impressed  e.m.f.  divided  by  impedance  E  -=-  Z. 

Impresed  e.m.f.  multiplied  by  admittance  E  X  Y. 

True  watts  divided  by  impressed  e.m.f.  times  power  factor 
(cosine  angle  of  lag  or  lead)   P -4-  (E  X  p.f.). 

Reactive  e.m.f.  divided  by  reactance. 

The  square  root  of  true  watts  divided  by  resistance 


1=  VP-i-R. 

Impedance,  represented  by  Z  or  z. 
Impressed  e.m.f.  divided  by  current  E  -*-  Z. 
Resistance  divided  by  power  factor  (cosine  of  lag  or  lead 

angle)   R  -=-  p.f. 
Reactance  divided  by  reactive  factor   (sine  of  lag  or  lead 

angle)    X  -r-  r.f. 
The  square  root  of  the  sum  of  the  squares  of  resistance 

and  reactance  VR2  +  X^. 
Resistance,  represented  by  R  or  r. 
Impedance  times  power  factor  (cosine  of  lag  or  lead  angle) 

Z  X  p.f. 

The  square  of  effective  e.m.f.  divided  by  true  watts  E,,2  -=-  p. 
Effective  e.m.f.  divided  by  current  Er  -*-  I. 
True  watts  divided  by  square  of  current  P  -=-  12. 
The   square   root   of   impedance   squared   minus   square   of 

reactance  VZ^  —  X-V 

Reactance  (inductive),  represented  by  Xx. 
6.28  times  inductance  times  frequency  2?rLf. 
Impedance  times  reactive  factor  (sine  of  lag  angle)  Z  X  r.f. 
Reactance  (condensive),  represented  by  Xc. 
1  divided  by  6.28  times  frequency,  times  capacity 


6.28  f  C 

Impedance  times  reactive  factor  (sine  of  lead  angle)  Z  X  r.f. 

Condensive  e.m.f.  divided  by  current. 
Admittance,  represented  by  Y  or  y. 

One  divided  by  impedance  1  -f-  Z. 

Current  divided  by  e.m.f.  I  -f-  E. 


418  PRACTICAL  APPLIED  ELECTRICITY 

The  square  root  of  the  sum  of  the  squares  of  conductance 

and  susceptance,  Y  =  VG2  +  B2. 
Susceptance,  represented  by  B  or  b. 
Admittance  times  sine  of  lag  or  lead  angle  (reactive  factor) 

Y  X  r.f. 

Sine  of  lag  or  lead  angle  divided  by  impedance,  r.f.  -r-  Z. 
The   square  root  of   the   square   of   admittance   minus   the 

square  of  conductance,  B  =  VY2 —  G2. 
One  divided  by  reactance  if  there  is  no  resistance  1  H-  X. 
Conductance,  represented  by  G  or  g. 
Admittance  times  cosine  of  lag  or  lead  angle  (power  factor) 

Y  X  p.f. 

Cosine  of  lag  or  lead  angle  divided  by  impedance  p.f.  -=-  Z. 
The   square   root  of  the   square   of  admittance   minus   the 

square  of  susceptance,  G  =  VY^  —  B2. 
One  divided  by  resistance  (for  direct  current)  1  -r-  R. 
Power  (true  watts),  represented  by  P. 
Effective  e.m.f.  times  current  Er  X  I. 
Impressed   e.m.f.   times    current   times    power   factor    E  X 

I  X  p.f. 

Square  of  current  times  resistance  12  x  R. 
Square  of  current  divided  by  conductance   (no  reactance) 

12 --G. 
Impedance    times    current    squared    times    power    factor 

Z  X  I2  X  p.f. 

Apparent  Watts,  represented  by  P. 
Impressed  e.m.f.  times  current  E  X  I. 
Square  of  current  times  impedance  12  X  Z. 
Square  of  current  divided  by  admittance  12  -5-  Y. 
Power  Factor. 

True  watts  divided  by  apparent  watts  P  -=-  (E  X  I). 
Resistance  divided  by  impedance  R  -f-  Z. 
Effective  e.m.f.  divided  by  impressed  e.m.f.  Er  -f-  E. 
Reactance  Factor. 

Reactance  divided  by  the  resistance  X  H-  R. 
Reactive  Factor. 
Wattles    volt-amperes    divided    by    the    total    volt-amperes 

XXl-^-ZXl  =  X^-Z  =  sine  of  the  angle  of  lag  or  lead. 


INDEX 

A 

PAGE 

Admittance  of  a  circuit 349 

Alternating-current  circuit 332 

addition  and  subtraction  of  vectors 338 

alternation  333 

chemical  and  heating  effects  of 334 

cycle  333 

definition  of  alternating  current 332 

determining  value  of  power  factor 354 

electromotive  force  required  to  overcome  resistance  339 
electromotive  force  required  to  overcome  resistance, 

inductance,  and  capacity 344 

factors  determining  value  of  a.  c 338 

frequency 333 

hydraulic  analogy  of  alternating  current 332 

hydraulic  analogy  of  capacity 342 

hydraulic  analogy  of  inductance 339 

impedance  of  a  circuit 347 

impedance  diagram 348 

impedances  in  parallel 349 

impedances  in  series 348 

instantaneous  power  in 353 

maximum,  average  and  effective  values  of  e.m.f....  336 

period  333 

phase 333 

phase  relation  of  current  and  potential  drops  in  a 

divided  circuit 352 

phase  relation  of  current  and  potential  drops  in  a 

series  circuit  351 

phase  relation  of  e.m.f.  to  overcome  inductance,  etc.  341 

problems  on 356 

reactance  of  a  circuit. .  347 


INDEX 

Alternating-current  circuit — continued  PAGE 

sine  wave  e.m.f 335 

synchronism 333 

total  e.m.f.  required  to  produce  a  given  alternating 

current    346 

vector    representation    of    alternating    e.m.f.'s    and 

currents    338 

wattmeter  indicates  true  power  in 355 

Alternating  current  machinery 358 

alternators    358 

connecting  receiving  circuits  to  a  three-phase  system  364 

induction    generator 384 

induction  motor 379 

measurement  of  power  in  single-phase  system 365 

measurement  of  power  in  three-phase  system 367 

measurement  of  power  in  two-phase  system 365 

relation  of  e.m.f.  and  current  in  "Y"  and  "A"  con- 
nected   armatures 362 

rotating  magnetic  field 378 

synchronizing    371 

synchronous    converter 385 

synchronous  motor 368 

transformer    372 

Alternation,  definition   of 333 

Alternators 358 

inductor'    358 

single-phase   360 

with  stationary  armatures 358 

with   stationary   fields 358 

three-phase    361 

Amalgamation    60 

Ammeter 122-132 

Ammeter,  calibration  of 163 

Ammeter  shunts 124 

Ampere,  definition  of 6-10 

Ampere-hour  meters 159 

Ampere-turns,  definition  of 94 

Angle  of  lag,  definition  of 182 

Angle  of  lead,  definition  of 182 

Armature  coil 227 

Armature  inductor 226 


INDEX 

PAGE 

Armature  reaction 180 

Armature  reaction,  means  of  reducing 183 

Armatures    219 

armature    core 219 

armature-core    stampings 220 

ventilation    221 

armature   windings 224 

armature    coil 227 

armature  inductor 226 

drum  windings 230 

element  of 227 

equipotential   connections 235 

front  and  back  pitch,  choice  of 234 

multiplex  windings   232 

number  of  commutator  segments 227 

number   of   paths   through 233 

pitch  of  winding  and  field  step 228 

re-entrancy    232 

ring   windings 229 

table 335 

brushes  and  brush  holders 223 

commutator    222 

commutator    risers 222 

construction  of 223 

Anode,  definition  of 126 

Artificial   magnets 77 

Automobile    motors 212 

Auto-transformer    377 

B 

Balanced  load 261 

Bichromate   cell 65 

Bonding,   definition  of 129 

Boosters    267 

Bremer  flaming-arc   lamp 304 

British  thermal  heat  unit,  definition  of 142 

Brushes  and  brush  holders 223 

Bunsen  photometer 308 

Bus-bars    270 


INDEX 
C 

PAGE 

Calculation   of   illumination 310 

Calculation  of  resistance  of  conductor 318 

Calculation   of   size   of   conductor   when   allowable   drop 

and  current  are  given 319 

Calibration    of   instruments 161 

ammeters    163 

voltmeters    161 

wattmeter    163 

Carbon  arc  lamp 294 

Carbon-filament    lamp . .  „ 299 

Cathion,    definition    of 126 

Cathode,   definition   of 126 

Chemical    depolarization 65 

Fuller   cell 66 

Grenet    cell 65 

Leclanche    cell 67 

Chemicals  used  in  cells  and  their  symbols 65 

Choice  of  material  to  use  as  conductor 317 

Circuit  breakers 273 

Circular  mil,  definition  of 28 

Closed-coil  windings 225 

Commercial  wheatstone  bridge 54 

Commutation  of  generator 185 

Commutator  pitch 229 

Compensated  wattmeter    155 

Compound  generators  in  parallel *. .  271 

Compound  motor 194 

Compound  motor,  characteristics  of 208 

Compound-wound  generator 179 

Concealed  "knob  and  tube"  work 325 

Condenser    145 

capacity  of 145 

connection  of  in  series  and  parallel 147 

dielectric    145 

problems    on 149 

relation    of    impressed    voltage,    quantity    and    con- 
denser  capacity 148 

Conductance  of  a  circuit 349 

Conductance  of  a  conductor 18 


INDEX 

PAGE 

Conductors   6 

Conductors,  area  of  circular 20 

Constant-current    distribution 258 

Constant-voltage    distribution 257 

Coulomb,  definition  of 6-9 

Counter  electromotive  force   199 

Cumulative    compound   motor 195 

Current,  definition  of 4 

Current  of  electricity 6 

Current,  uniformity  of  in  series  circuit 35 

Cycle,  definition  of 333 

D 

Daniell    cell 64 

Daniell  cells,  electro-chemical  depolarization  of 67 

D'Arsonval  ammeters 134 

D'Arsonval  galvanometer    133 

D'Arsonval  voltmeters 134 

Dead-line  release 205 

Diamagnetic,   definition   of 82 

Dielectric    145 

Differential    compound    motor 195 

Differential    shunt. . . ., 298 

Direct-current  dynamos,  diseases  of . . ' 280 

Direct-current  generator 166 

adaptability   of 189 

armature  of  a  dynamo 173 

armature    reaction 180 

back  turns 182 

building   up    of 187 

capacity    of 186 

commercial  rating  of 191 

commutation    of 185 

compound-wound    179 

cross-turns    182 

efficiency    of 190 

external  characteristics  of 187 

losses  in 189 

magnetic  field  of  a  dynamo 173 


INDEX 

Direct-current  generator — continued  PAGE 

magnetic    leakage 17* 

multiple-coil   armatures 171 

problems    on 191 

reducing   armature   reaction 183 

self-excitation    of 177 

separate  excitation  of 177 

series-wound 178 

simple  alternator. 168 

simple  direct-current  dynamo 170 

simple  dynamo 166 

shunt-wound    178 

values  of  induced  e.m.f.  in  armature  winding 176 

Direct-deflection  method  of  measuring  resistance 50 

Direct-current    motors 193 

adaptability   of 208 

armature    reaction    in 196 

automobile   212 

characteristics    of 207 

combined  starting  and  field-regulating  rheostats...  206 

compound 194 

construction  of  209 

counter   electromotive    force 199 

dead-line   release 205 

efficiency  of 215 

elevator  and  crane 214 

Fleming's    left-hand    rule 193 

fundamental  principle   of 193 

interchangeability  of  motor  and  generator 193 

interpole  motor 203 

mechanical   output   of 198 

normal   speed   of 199 

overload    release 206 

position  of  brushes  on 197 

problems    on 217 

railway 210 

regulating  speed  of 200 

series 194 

shunt 194 

speed    regulation 206 

starting    204 


INDEX 

Direct-current  motors — continued  PAGE 

starting    boxes 205 

torque  exerted  on 198 

Ward  Leonard  system  of  speed  control 203 

Diseases  of  direct-current  dynamos 280 

dynamo  fails  to  generate 290 

heating  of  armature 284 

heating  of  bearings 285 

heating  of  field  coils 284 

motor  runs  backward  or  against  the  brushes 290 

motor  stops 289 

noise    287 

sparking  at  brushes  caused  by  excessive  current  in 

armature  due  to  overload 282 

sparking  at  brushes  due  to  fault  of  armature 283 

sparking  at  brushes  due  to  fault  of  brushes 280 

sparking   at   brushes    due    to    fault   of   commutator 

or   magnetic   field 281 

speed  too  high 288 

speed   too    low 289 

suggestions  and  precautions 292 

Disk    windings 224 

Distribution  curves : 310 

Distribution   and    operation 257 

boosters    267 

circuit   breakers 273 

constant-current    distribution 258 

compound  generators  in  parallel 271 

constant-voltage   distribution 257 

drop  in  potential  in  the  neutral  wire 261 

dynamotors    265 

Edison  three-wire  system  of  distribution 259 

ground   detectors 275 

instructions  for  starting  a  generator  or  motor 276 

motor  generators,  or  balar  cers 267 

operation  of  compound  motors 273 

operation   of  generators   and   motors   for   combined 

output    269 

operation  of  series  motors  in  series  and  parallel....  272 

operation  of  shunt  motors  in  series  and  parallel 272 

rheostat 274 


INDEX 

Distribution  and  operation — continued  PAGI) 

series  generators  connected  for  combined  output. ...  27(  j 

series-parallel  system  of  distribution 25i 

shunt  generators  connected  for  combined  output 26i 

starting  and  stopping  compound  generators  that  are 

operating  in  parallel 27£ 

switchboard    27£ 

switches 27J 

three-wire  generators   26; 

Drop  in  potential  in  the  neutral  wire 261 

Drum  windings  224 

lap    23( 

progressive    231 

retrogressive    231 

wave    231 

Dry  cells  6£ 

Dynamic  brake 21E 

Dynamotor  as  an  equalizer 26£ 

Dynamotors    26!; 

E 

Eddy  currents Ill 

Eddy-current  loss 11£ 

Edison  chemical  meter 15J 

Edison  storage  battery 241 

care  of 25( 

chemistry  of   24J 

Edison  three-wire  system  of  distribution 25i 

Effect  different  colored  walls  have  upon  general  illumi- 
nation      3: 

Electric  heaters   32< 

Electric  generators  and  motors 33( 

Electric  lamp    29' 

Electric  lighting   29- 

Bremer  flaming-arc  lamp 30^ 

Bunsen  photometer  30* 

calculation    of    illumination 31( 

carbon  arc  lamp 29^ 

carbon-filament  lamp 291 

distribution   curves    .  31( 


INDEX 

ilectric  lighting— continued  PAGE 
effect  different  colored  walls  have  upon  general  illu- 
mination      315 

electric  lamp  294 

flaming  arc 304 

glow  lamp    - 299 

heftier   lamp    307 

mercury  vapor  lamp 304 

metalized  carbon-filament  or  gem  lamp 300 

Moore  tube    300 

multiple  arc  lamps 296 

Nernst  lamp 303 

photometry    307 

regulation  of  arc  lamps  on  constant-voltage  and  con- 
stant-current circuit    295 

series  arc  lamps 297 

shades,  reflectors,  and  diffusers 314 

specific  consumption  of  lamps 309 

tantalum  lamp 300 

tungsten   lamp    301 

units  of  illumination 307 

vapor   lamp    303 

Electric  wiring   316 

calculation  of  resistance  of  conductor 318 

calculation  of  size  of  conductor  when  allowable  drop 

and  current  are  given 319 

choice  of  material  to  use  as  conductor 317 

concealed  "knob  and  tube"  work 325 

electric  generators  and  motors 330 

electric  heaters    329 

electrical  inspection    330 

factors  determining  size  of  conductors 316 

installing  arc  lamps  and  fixtures 329 

interior  conduit  and  armored  cable  work 326 

location  of  outlets,  switches,  and  distributing  board.  328 

methods  of  wiring  and  rules  governing  s?me 322 

motor  wiring  formula 321 

moulding  work   324 

open,  or  exposed,  work 323 

service  wires  327 

wiring  in   general 316 


INDEX 

PAGE 

Electrical  circuit  1 

compared  with  hydraulic  circuit 5 

conductors    6 

coulomb,  ampere,  ohm,  and  volt 9 

current  of  electricity 6 

derived  units  15 

electrical  force  11 

electrical  power  13 

electrical  quantities    ,  6 

electrical  work  or  energy 12 

electromotive  force  7 

fundamental  units  15 

hydraulic  analogy  of 2 

insulators    7 

Joule,  unit  of  electrical  work 12 

kilowatt 14 

kilowatt-hour    15 

mechanical  horse-power    14 

*     Ohm's  Law 8 

resistance    6 

watt-hour    15 

Electrical  force,  definition  of 11 

Electrical  inspection  330 

Electrical  instruments   121 

ammeter   122 

ammeter  shunts  124 

calibration  of  instruments 161 

galvanometer    122 

measurement  of  power 151 

operation  depending  on  electro-chemical  effect 125 

electrolysis    125 

electroplating 127 

electrotyping   128 

polarity  indicator    128 

weight  voltameter   129 

operation  depending  on  electrostatic  effect 145 

electrostatic  voltmeter 150 

condenser   145 

operation  depending  on  heating  effect 141 

hot-wire  instruments  .  143 


INDEX 

Electrical  instruments— continued  PAGE 

operation  depending  on  magnetic  effect 132 

electro-dynamometer 139 

magnetic  vane  ammeter  or  voltmeter 138 

plunger  type  ammeter  or  voltmeter 137 

tangent  galvanometer    132 

Thomsen  inclined-coil  instruments 138 

voltmeter    122 

Electrical  power,  unit  of 13 

Electrical  quantities  6 

Electrical  units    .' 12-16 

derived  units 15 

fundamental  units  15 

horse-power    14 

Joule    12 

kilowatt 14 

kilowatt-hour    15 

systems  of  units 16 

watt 13 

watt-hour  15 

Electrical  work  or  energy 12 

Electricity,  definition  of 1 

Electro-chemical  depolarization 67 

Electrodynamometer 139 

Electrodes,  definition  of 125 

Electrolysis    125-127 

of  copper  sulphate 127 

definition  of 125 

Electrolyte   241 

Electrolytic  action,  prevention  of 128 

Electrolytic  cell,  definition  of 125 

Electromagnet 98 

Electromagnetic  induction   102 

currents  induced  in  coil. .- 105 

.currents  induced  in  conductor 102 

eddy  currents   117 

induced  pressures,  rules  for 116 

inductance    114 

Lentz's  law   115 

magnitude  of  induced  e.m.f 106 

mutual  induction 113 


INDEX 

Electromagnetic  induction — continued  PAGE 

non-inductive  circuit  119 

primary  coils  109 

secondary  coil 109 

self-induction    113 

Electromagnetism    86 

direction  of  an  electromagnetic  field 86 

electromagnet 98 

law  of  traction  101 

magnetic  field  around  conductor  carrying  current...  86 

magnetomotive  force   93 

permeability 92 

problems  on    97 

reluctance 95 

rules  for  determining  direction  of  field 88 

solenoid  89 

strength  of  magnetic  field 89 

toroid 92 

Electromotive  force    7 

Electromotive  force  in  a  circuit,  effective 38 

Electromotive  force  of  a  cell,  factors  determining 62 

Electromotive  force  and  potential  difference 7 

Electroplating 127 

Electrostatic  voltmeter   150 

Electrotyping 128 

Elevator  and  crane  motors 214 

Equalizer 271 

Evershed  ohmmeter,  principle  of 56 

F 

Factors  determining  size  of  conductors 316 

Feeder  valve  306 

Field  rheostat 178 

Flaming  arc    ; 304 

Flashing    300 

Fleming's  motor  rule 193 

Foot-candle   307 

Frequency,  definition  of 333 

frequency  changer  384 

Friction  brake 214 

Fuller  cell  .  64 


INDEX 
G 

PAGE 

Galvanometer    122 

Gauss,  definition  of 94 

Generator  panels  and  feeder  panels 273 

Gilbert,   definition   of 94 

Glow  lamp 299 

Grenet  cell  63-65 

Ground  detectors  275 

H 

Heating  effect  of  a  current,  commercial  applications  of.  .  142 

Hefner  lamp 307 

Hefner  unit 307 

Henry,  unit  of  inductance 115 

Horse-power 14 

electrical  14 

mechanical    14 

Horseshoe  magnet 85 

Hot-wire  instruments 143 

Hydraulic  analogy  of  electrical  circuit 2 

Hydraulic  circuit  compared  with  electrical : 5 

Hydrometer   242 

Hysteresis    98 

definition  of 83 

loss    99 

I 

Induced  electromotive   force ,V« 102 

direction  of   107 

magnitude  of ' 106 

rules   for   determining 109 

in  secondary  coil 109 

Induced  pressures,  rules  for 116 

Inductor  alternators   358 

Inductance    114 

Induction  generator 384 

Induction  motor  379 

methods  of  starting 382 


INDEX 

Indication  motor — continued  PAGE 

operation  of 381 

rotor 380 

speed  regulation  of 381 

"squirrel-cage"  type   380 

stator    380 

Installing  arc  lamps  and  fixtures 329 

Instructions  for  starting  a  generator  or  motor 276 

Insulators    7 

Integrating  wattmeters   159 

Interior  conduit  and  armored  cable  work 326 

Internal  resistance 62 

International  ohm,  definition  of 10 

Interpole  motor 203 

Ions,  definition  of , 126 

J 

Joule,  unit  of  electrical  work  and  energy 12 

K 

Kicking  box 325 

Kilovolt,  definition  of 10 

L 

Lalande  cell    64 

Lead  storage  cells 237 

action  of,  while  charging 238 

action  of,  while  discharging 238 

Leakage  coefficient 176 

Leclanche   cell    63 

Lentz's  law 115 

Location  of  outlets,  switches, 'and  distributing  board. . . .  328 

Logarithms 390 

characteristic,  definition  of 391 

common  system  of 390 

definition  of 390 

to  find  a  number  whose  log  is  given 391 

how  to  obtain  log  of  a  number  from  table 391 

laws  of  indices 390 

mantissa,  definition  of 391 


INDEX 
M 

PAGE 

Magnet    '. 77 

artificial 77 

permanent    84 

poles  of 78 

currents  induced  in  a  conductor  by 102 

Magnetic  attraction  78 

Magnetic  circuit,  materials  used  in  construction  of 175 

Magnetic  field  of  a  dynamo 173 

air  gap 174 

armature  core  174 

field  cores 173 

pole  face    174 

pole  pieces  174 

yoke   173 

Magnetic  field  of  force 80 

distortion  of    81 

making  of  81 

Magnetic  field,  strength  of 89 

Magnetic  force 79 

Magnetic  flux    94 

Magnetic  induction   , 82 

Magnetic  leakage  176 

Magnetic  lines  of  force 80 

Magnetic  meridian    78 

Magnetic  needle  78 

Magnetic  repulsion   78 

Magnetism 77 

magnet    77 

magnetic  attraction  78 

magnetic   field    80 

magnetic  force  . 79 

magnetic  lines  of  force 80 

magnetic  induction 82 

magnetic  needle  78 

magnetic  repulsion   78 

magnetizable  metals 79 

molecular  theory  of 83 

retention  of  magnetization 82 

Magnetizable   metals    79 


INDEX 

PAGE 

Magnetization  curve   187 

Magnetization,  retention  of 82 

Magnetomotive  force  93 

Maximum   demand  meters. 160 

Maxwell,  definition  of. 94 

Mean  horizontal   candle-power 307 

Mechanical  depolarization 65 

Megohm,  definition  of 10 

Mercury  vapor  lamp 304 

Metalized  carbon-filament  or  gem  lamp 300 

Methods  of  wiring  and  rules  governing  same 322 

Microhm,  definition  of 10 

Mil-foot  resistance    29 

Millivolt,  definition  of 10 

Molecular  theory  of  magnetism 83 

Moore  tuhe    306 

Motor-generators,    or   balancers 267 

Motor  wiring  formula 321 

Moulding  work   324 

Multiple  arc  lamps 296 

Multipliers   136 

Multiplex  windings   232 

Mutual  induction   113 

N 

Negative  booster   268 

Negative  grid    238 

Nernst  lamp    303 

Neutral  wire   260 

No-load  current    373 

Non-lead  storage  cells 246 

Non-inductive  circuit   119 

O 

Ohmmeter  56 

Ohm's  law 8 

problems  on 10 

Open-coil    windings 226 

Open,  or  exposed,  work 323 


INDEX 

PAGE 

Operation  of  compound  motors 273 

Operation  of  generators  and  motors  for  combined  output.  269 

Operation  of  series  motors  in  series  and  parallel 272 

Operation  of  shunt  motors  in  series  and  parallel 272 

Overload  release    206 

Oversulphation    243 

P 

Panels    273 

Paramagnetic,  definition  of 82 

Period  of  an  e.m.f.,  definition  of 333 

Permanent  magnets,  application  of 84 

Permeability    92 

Phase,   definition   of 333 

Photometer    307 

Photometer  bench 309 

Photometry    307 

Polarity,   definition  of 78 

Polarity  indicator   128 

Polarity  of  solenoids 91 

Polarization   60 

chemical  means  of  prevention 61 

electro-chemical  means  of  prevention 62 

mechanical  means  of  prevention 61 

Poles  of  a  magnet 78 

Portable  storage  batteries 251 

Positive  grid   238 

Potential  difference,  relation  of,  to  resistance 36 

Power,   measurement  of 151 

Power  and  energy  calculations,  problems  on 16 

Power  factor  354 

Pressure,  definition  of 

Primary  batteries  58 

amalgamation    60 

cell  requirements 70 

chemical  action  in  battery 59 

chemical  depolarization  65 

chemicals  used  in  cells 65 

closed-circuit  cell  63 


INDEX 

Primary  batteries — continued  PAGE 

double-fluid  cell   64 

dry  cells   68 

electro-chemical  depolarization  67 

electromotive  force  of  a  cell 62 

grouping  of  cells,  problems  on 74 

internal  resistance 62 

local  action  in  battery 60 

mechanical  depolarization    65 

open-circuit  cell   63 

parallel  connection  of  cells 72 

polarization    60 

primary  cell   63 

secondary  cell  63 

series  connections  of  cells 70 

series  and  parallel  combinations  of  cells 73 

single-fluid  cell 64 

standard  cells   69 

voltaic  cells  58 

Primary  cells,   forms  of 64 

Prony  brake 216 

R 

Railway  motors  and  their  control 210 

Reactance  coil 296 

Re-entrant  windings 232 

Regulation   of  arc   lamps  on   constant-voltage   and   con- 
stant-current circuit   295 

Relative  conductivity  of  a  material 30 

Relative  resistance  of  a  material 30 

Reluctance  of  magnetic  circuit 95 

Resistance,  calculation  of 18 

area  of  circular  conductors 20 

changes  with  temperature 21 

from  dimensions  and  specific  resistance 31 

due  to  change  in  temperature 24 

meaning  of  (K) 28 

mil-foot  resistance  29 

relation  to  physical  dimensions 27 

relation  between  square  and  circular-mil  measure. ..  30 


INDEX 

Resistance,  calculation  of — continued  PAGE 

relative  conductivity 30 

relative  resistance  30 

specific  resistance 28 

temperature  coefficient 21 

varies  inversely  as  cross-section  of  conductor 19 

varies  directly  as  the  length  of  conductor 18 

Resistance,  definition  of 4 

Resistance,  measurement  of 44 

commercial   Wheatstone  bridge 54 

by  comparison   47 

direct-deflection    method     50 

drop  in  potential  method 44 

ohmmeter    56 

series  voltmeter  method 48 

slide-wire  Wheatstone  bridge 52 

Resuscitation  from  apparent  death  from  electric  shock..  386 

Reverse-current    274 

Rheostats 205,  274 

Right-hand  screw  rule 88 

Ring  windings    224 

series-connected'  wave-wound    230 

spirally-wound 229 

S 

Screen    308 

Self-excitation  of  generator 177 

Self-induction    113 

Separate  excitation  of  generator 177 

Series  arc  lamps 297 

Series  and  divided  circuits 34 

effective  e.m.f.  in  a  circuit 38 

parallel  or  multiple  grouping 39 

problems  on 43 

relation  of  p.d.  to  resistance 36 

resistance*  of 37 

series   grouping    , 34 

series  and  parallel  combinations 42 

uniformity  of  current 35 

Series  generators  connected  for  combined  output 270 


INDEX 

PAGE 

Series  motor 194 

characteristics   of 207 

Series-parallel   system  of  distribution 259 

Series  voltmeter  method  of  measuring  resistance 48 

Series-wound  generator   178 

Service  wires    327 

Shades,  reflectors,  and  diff users 314 

Shunt  generators  connected  for  combined  output 269 

Shunt  motor 194 

characteristics  of 207 

Shunt-wound  generator   178 

Single-phase  alternator    360 

Slide-wire  Wheatstone  bridge,  principle  of 52 

Solenoid   89 

permeability    92 

polarity  of 91 

toroid    92 

Specific  consumption  of  lamps 309 

Specific  inductive  capacity 145 

Speed  regulation  of  a  motor 206 

Specific  resistance 28 

Square  and  circular-mil  measure,  relation  between 30 

Standard  cells  69 

Starting  and  stopping  compound  generators  that  are  op- 
erating in  parallel 278 

Storage  batteries   237 

to  aid  generators  in  carrying  maximum  load 253 

capacity  of  241 

commercial  application  of 250 

containing  vessel  and   separators 242 

Edison   247 

in  electrical  laboratories 251 

electrolyte    241 

hydrometer    242 

lead  cell   237 

management  of 245 

non-lead  cell   246 

portable    251 

to  put  out  of  service 246 

sulphation 243 


INDEX 

Storage  batteries — continued  PAGE 

to  supply  energy  during  certain  hours 253 

to    supply    energy    for   electrically    driven    vehicles 

and    boats    255 

storage  battery  grids 239 

storage  cell   237 

in  telephone  and  telegraph  work 252 

for  train  lighting 252 

troubles  and  their  remedies 244 

buckling  of  plates 245 

corrosion  of  plates 245 

loss  of  capacity 244 

loss  of  voltage 245 

shedding  of  active  material 245 

used  in  changing  voltage 254 

used  in  subdividing  voltage  of  a  generator 255 

Storage   battery   grids 239 

comparison  of  Plante  and  Faure 240 

example  of 239 

Faure   process    239 

Plante   process    239 

Sulphation    243 

Susceptance   of  a   circuit 349 

Switchboard    273 

Switches    275 

Synchronism,  definition  of 333 

Synchronizing 371 

Synchronoscope    372 

Synchronous   converter    385 

Synchronous  motor  368 

operation   of    370 

starting 370 

synchronizing 371 

T 

Table 

approximate  specific  consumption  of  different  type 

lamps    310 

capacity  of  storage  battery,  percentage  variation  of.  241 
centigrade  and  Fahrenheit  thermometer  scales,  com- 


INDEX 

Table — continued  PAGE 

parison  of    400 

constants  to  be  used  in  calculating  illumination  on 

horizontal  plane   below  lamp 312 

copper  wire  table  of  American  Institute  of  Electrical 

Engineers    402-405 

electro-chemical  equivalents    130 

factors  for  obtaining  effective  illumination 315 

hysteretic  constant,  value  of,  for  different  materials.  100 

lap-wound  drum  armature  windings 410 

logarithms   of   numbers 394,  395 

mensuration  equations  396 

metric  and  English  measures,  relation  of 399 

primary  cells / 64 

required  illumination  for  various  classes  of  service.  313 

ring  armature  windings 408 

specific  inductive  capacities '. 146 

specific   resistance    data 29 

symbols  for  electrical  apparatus 398 

symbols  for  wiring  plans 414 

temperature   coefficients    22 

temperature  coefficient  of  copper 23 

trigonometrical  functions   397 

units  in  English  and  metric  systems,  relation  of 16 

v/ave- wound  drum  armature  windings 409 

wire,  carrying  capacity  of 406 

wires,  equivalent  cross-section  of  different  size 400 

wire  gauzes   401 

wiring  table  for  2  per  cent  loss  on  a  50-volt  circuit. .  411 

wiring  table  for  2  per  cent  loss  on  a  110-volt  circuit.  412 

wiring  table  for  2  per  cent  loss  on  a  220-volt  circuit.  413 

wire  which  will  fuse  with  given  current,  diameter  of.  407 

Tangent  galvanometer  132 

Tantalum  lamp  300 

Temperature  coefficient,  definition  of 21 

Thomson  watt-hour  meter 158 

Three-phase  alternator 361 

Three-wire  generators    263 

Toroid 92 

Traction,   law   of 101 

Transformer 372 


INDEX 

Transformer — continued  PAGE 

action  of,  on  load 373 

action  of,  without  load 372 

actual  e.m.f.  and  current  relations  in 374 

auto-transformer 377 

constant-current     377 

constant-potential    377 

core  type 376 

current   377 

ideal  e.m.f.  and  current  relations  in 373 

methods  of  cooling 377 

polyphase   376 

shell  type 376 

single-phase   376 

vector  diagram  of 375 

Transposition,  definition  of 113 

Tungsten  lamp 301 

U 

Unbalanced  load 261 

Under-load , 274 

Units  of  illumination 307 

V 

Vapor  lamp   303 

Voltaic  battery  59 

amalgamation    60 

chemical  action  in 59 

local  action    , 60 

polarization    60 

Voltaic  cell 58 

Volt,  definition  of 10 

Voltameter  

adaptability  of 131 

definition  of 126 

Voltmeter 122 

calibration  of  .  161 


INDEX 
W 

PAGE 

Watt-hour  meters   156 

Wattmeter    153 

adaptability  of .* 156 

calibration  of 163 

compensated    155 

principle  of   153 

Weston    155 

Whitney    154 

Weight  voltameter 129 

Weston  portable  voltmeter 137 

Weston  wattmeter 155 

Wheatstone  bridge   

commercial    54 

slide-wire    52 

Whitney   wattmeter    1 54 

Wire  gauges    32 

Wiring  in  general 316 

Wright  demand  meter 160 


Zero  load   372 


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OCT    9   1933 
.5  19?3 
121934 

""' 


NOV 


tf'47 


LD  21-100m-7,'33 


VB   ,'5790 


389482 


.UNIVERSITY  OF  CALIFORNIA  LIBRARY 


